If baking immediately, preheat the oven to 350 degrees.
Caramelize the leeks and onions: Melt butter in a large pan over medium heat. If baking your strata in a cast iron skillet, you can use the same pan. Add leeks and onions and season with salt and pepper. Cook, stirring occasionally, until they’re soft and beginning to brown, 15-20 minutes. Remove from heat and transfer to a small bowl.
While the leeks and onions are cooking, make the egg mixture: In a medium bowl, whisk eggs until no streaks remain. Whisk in the milk, 2 tsp salt, 3 tbsp za’atar, and a few cracks of black pepper.
Assemble the strata: In a 12-inch cast iron skillet or 9x13 inch casserole dish, lay down a layer of broken matzo to cover the bottom of the pan, about two matzo boards’ worth. Over the matzo, sprinkle a third of the caramelized leeks and onions, a third of the mozzarella, a third of the feta, and a third of the parsley. Repeat the layering process two more times. If baking the next morning, cover with plastic wrap and refrigerate, and refrigerate the egg mixture in a covered container.
Bake the strata: Pour the egg mixture over the pan until most of the strata is submerged, leaving a thin half-inch layer exposed at the top. Bake 30-40 minutes if baking immediately, or 60-70 minutes if baking after refrigeration, until the eggs have set and the edges are a deep golden brown. Let cool slightly, serve, and enjoy!
