Preheat the oven to 400 degrees F. Line a pizza stone or baking sheet with parchment paper.
Mix the ricotta, oregano and red paper flakes in a small bowl. Add a small pinch of salt and pepper.
Unroll the pie crust onto the prepared pizza stone or baking sheet. Spread the ricotta mixture in the center of the dough, leaving a 1 1/2-inch border. Top with the mozzarella. Lay the tomato slices on top of the mozzarella, overlapping them if necessary. Fold the edge of the dough over the filling. Beat the egg in a small bowl with 1 teaspoon water. Brush the dough with the egg wash.
Bake until the crust is golden brown and shiny, 30 to 35 minutes. Cool for 10 minutes before serving. Garnish with basil.
For a meaty topping, top with sliced prosciutto during the last 5 minutes of baking.