Preheat oven to 400F. Line a 9x9-inch baking pan with parchment.
Beat egg in a large bowl. Set aside.
Place broccoli, Italian seasoning and salt in the bowl of a food processor. Whirl until very finely chopped (you should have about 2 cups). Scrape into bowl with egg. Add 1/2 cup mozzarella and parmesan. Stir to combine. Press into prepared baking pan.
Bake until set, about 20 minutes. Brush with garlic butter then sprinkle with remaining 1 cup mozzarella. Return to oven and bake until cheese is melted and just starting to turn golden-brown, 5 to 10 minutes more. Sprinkle with parsley and chili flakes.