Heat the butter and 1 tablespoon of the oil into a large sauté pan with a lid and place over medium-high heat. Once the butter starts to foam, add the leeks, 1/2 teaspoon of salt, and plenty of pepper. Fry, stirring frequently, until the leeks are soft, about 3 minutes. Add the vegetable broth, lemon, and cumin. Bring to a boil and cook until most of the broth has evaporated, 4 to 5 minutes. Add the spinach and fold in until wilted, about 1 minute.
Reduce the heat to medium. Use a large spoon to make 6 indentations in the mixture. Break 1 egg into each space. Sprinkle the eggs with a pinch of salt, dot the feta around the eggs, then cover the pan. Simmer until the egg whites are set but the yolks are still runny, 4 to 5 minutes. Meanwhile, mix the za’atar with the remaining 1 tablespoon of oil.
Brush the za’atar over the eggs. Serve at once, straight from the pan.
