Divide dough in half. Working with one piece at a time, roll or stretch out each piece into 10 to 12 rounds (as big as your largest ovenproof skillet).
Preheat broiler. Pour enough olive oil into a large skillet to thickly coat bottom of pan, about 1/8-inch deep. Heat pan on medium-high until oil starts to shimmer. Place 1 round of dough in pan and cook until bottom is crisp and browned, being careful not to let it burn, about 3 minutes.
Flip over dough and top browned side with half of the tomato sauce, mozzarella, and basil. When bottom is browned, transfer pan to oven until cheese begins to melt, 2 minutes. Remove from oven and transfer pizza to a serving platter. Repeat with remaining dough and ingredients.