Wipe the portobello mushrooms clean using barely moistened paper towels. Remove the stems, then slice off the excess mushroom rim that curls over the gills. (You are making sure the stem side has a flat surface so it will sear properly.) Reserve the stems and scraps for use in Step 2. Brush the portobello mushroom caps on both sides with 3 tablespoons olive oil and season generously with salt and pepper. Heat 2 tablespoons olive oil in a large (12-inch) nonstick skillet over medium-high and cook the mushrooms, gill-side down, until caramelized, 4 to 5 minutes, then flip and cook until softened, about 4 more minutes. Transfer to a wire rack, gill-side down, to cool.
Prepare the mushroom filling: Separate and reserve any mushroom stems. Roughly chop about two-thirds of the mixed mushrooms, then working in batches, transfer the roughly chopped mushrooms to a food processor and pulse until chopped into small pieces. (They should range from 1/4 inch to 1/2 inch in size.) Transfer the chopped mushrooms to a large bowl. By hand, finely chop the remaining mixed mushrooms and stems and the reserved portobello mushroom stems and trimmings into 1/4-inch pieces; add them to the large bowl. (Chopping most of the mixed mushrooms in the food processor will save you some time, but you’ll want to chop some by hand for texture.)
Prepare an ice bath in a large bowl. (You’ll use this to quickly cool the cooked mushrooms in Step 4. If preparing in advance, you can simply let the mixture cool to room temperature, then refrigerate.) Wipe out the skillet. Working in two batches, warm 1/4 cup olive oil over medium-high heat. Add about half the mushrooms, shallots, garlic and rosemary, and season lightly with salt and generously with pepper. (You’ll add soy sauce later, so avoid overseasoning at this stage.) Cook, stirring occasionally, until caramelized and tender, about 10 minutes. Transfer to a medium bowl and repeat with the remaining 1/4 cup oil and the remaining mushrooms, shallots, garlic and rosemary.
Once the second batch of chopped mushrooms is cooked and caramelized, return the first batch to the skillet. Add the port, soy sauce and thyme leaves and cook over medium-high, stirring occasionally, until the liquid evaporates, 3 to 5 minutes. (If using balsamic vinegar instead of port, reduce the cook time to 1 to 2 minutes.) Transfer the mushroom mixture back to the medium bowl and stir in the walnuts. Set the bowl over the prepared ice bath to cool, stirring occasionally, at least 20 minutes.
Prepare the cider-caramelized onions: Wipe out the skillet, then melt the butter over medium heat. Add the onions, sprinkle with the sugar, salt and pepper, and cook, stirring occasionally, until starting to soften, about 5 minutes. Add the cider and cook, stirring every few minutes, until the liquid evaporates and the onions are caramelized, about 15 minutes. Stir in the vinegar, if using, then transfer to a bowl to cool.
Heat the oven to 400 degrees. Place a large piece of parchment paper on your work surface and lightly dust it with flour. Unfold your thawed puff pastry and set it on the parchment. Using a lightly floured rolling pin, roll the pastry out into a 13-by-16-inch rectangle. Transfer the parchment paper and puff pastry to a large sheet pan. Rotate the sheet pan, if needed, so that one of the 16-inch sides is closest to you. Arrange half the cooked mushroom mixture in a strip in the center of the puff pastry (it should be about 4-by-10 inches), leaving a 1½-inch border at the ends. Arrange the caramelized onions in a single, 3-inch-wide strip on top of the mushroom mixture, leaving about ½ inch of the mushrooms exposed on both sides. Lay the portobello mushrooms on top of the onions in a single line, stem-side down. (If the portobellos are too large to all fit in a row, square off edges so the cut sides lay snugly without overlapping.) Spoon the remaining mushroom mixture on top of the filling, covering the portobello mushrooms, then gently pack the mushroom mixture to form an even layer on top. (You can shape this the same way you might shape a freeform meatloaf.)
To assemble, lift one side of the puff pastry over the mushroom filling to almost completely cover it. Brush the surface of the puff pastry covering the mushrooms with the beaten egg. Lift the remaining puff pastry flap over the egg-washed puff pastry, gently stretching it if need be to create a second layer of puff pastry on top, then gently press the top layer of pastry onto the lower layer using your fingertips to seal. Brush the insides of the short ends of the puff pastry and press to seal. Trim any parchment paper that extends beyond the sheet pan.
Brush the exposed puff pastry on top with the remaining beaten egg. Decorate the top of the puff pastry as you like: Create a cross-hatch pattern by gently slicing through only the top layer of puff pastry in parallel lines, then cutting parallel lines in another direction. (Apply very little pressure, as you only want to cut through the top layer of puff pastry, not the second layer.) You can also slice small decorative vents in the puff pastry (be sure to slice all the way through both layers of puff pastry), or top with additional strips or shapes made from egg-washed puff pastry.
Transfer to the middle rack in the oven and bake until puff pastry is deep golden and flaky, 45 to 50 minutes. Let cool slightly on the baking sheet, about 10 minutes.
While the Wellington bakes, prepare the optional port reduction: In a medium saucepan, heat the oil over medium. Add the shallot, garlic and peppercorns, and cook, stirring occasionally, until softened, about 3 minutes. Add the port, stock and thyme, and cook over medium-high until the sauce is thick enough to coat the back of a spoon, 25 to 30 minutes. Strain the sauce, discarding the solids. (You should have about 1/2 cup sauce.) Cover and set aside until ready to serve. When ready to serve, warm the sauce over medium. Once warmed, whisk in the butter, season to taste with salt and pepper and serve.
To serve the mushroom Wellington, cut it crosswise into 8 even slabs. (Each slab will include a pretty cross-section showcasing the halved portobello mushroom in the center; this is considered the presentation side.) Serve each piece presentation-side up. Pass with port reduction for drizzling on top
