Preheat oven to 450 degrees. Turn a large baking sheet upside down; rub with oil. Using your hands, crush tomatoes into a pulp in a small bowl; season with salt and pepper.
Spread crushed tomatoes on pizza shells; sprinkle with red-pepper flakes. Bake until crusts are golden, 18 to 20 minutes.
In a bowl, toss arugula with Pecorino; top pizzas with salad. Drizzle with vinegar and, if desired, oil.