Place pita breads on a large baking sheet. Top each pita flatbread with about 3/4 cup roasted butternut squash. Add half a diced tomato on top. Sprinkle each pita with about 1/2 cup shredded cheddar cheese. Add some fresh parsley on top of the shredded cheese. Make a "nest" in the middle of eat pita and crack an egg into it. Season with a pinch of salt and freshly ground black pepper.
Bake at 375F for 10-18 minutes, or until the egg is cooked how you like it (see notes). Carefully transfer flatbreads to a plate and cut into four wedges to serve.
Pita breads or naan breads work great for this recipe. Use whole wheat if you can find it.
Cooking time for the egg might vary depending on your oven. If the flatbreads are getting too brown and crisp but the eggs are still too runny, turn down the oven and bake at 300F until the eggs are cooked to your liking.