Unfold dough. In a lightly oiled 12- to 14-inch pizza pan or on a 14- by 17-inch baking sheet, pat dough into a 12-inch-wide round with a slightly thicker 1/2-inch-wide rim.
Bake crust on lowest rack in a 425° oven until lightly browned on the bottom, 6 to 8 minutes (5 to 6 minutes in a convection oven).
In a bowl, combine tomato paste, 2 tablespoons water, and oregano.
Spread tomato mixture over crust, but not rim. Sprinkle with capers. Drop shredded mozzarella cheese in clusters onto tomato mixture, then sprinkle with parmesan.
Return pizza to lowest oven rack and bake until mozzarella softens, about 3 minutes (2 minutes in a convection oven). Scatter basil leaves and chili flakes over pizza.