Fill a Dutch oven with 3 inches of vegetable oil. Place the pot over medium heat and bring the oil up to 350 degrees F on a deep-fry thermometer.
Meanwhile, roll out the pizza dough on a lightly floured surface to 1/4 inch thick. Using a pizza cutter, cut 2-by-1-inch pieces of pizza dough. Carefully lower a few of the pieces into the oil. Fry, flipping occasionally, until golden brown, bubbly and crispy, 2 to 3 minutes. Drain well on a paper towel-lined tray. Season with a pinch of salt. When drained, place in a bowl and sprinkle with 1/4 cup of the Pecorino and 1/4 teaspoon black pepper. Continue the process with the remaining dough, layering in the bowl as you go.