Prepare a gas or charcoal grill for indirect grilling.
Divide the dough into four pieces and shape each one into a ball. Let rest for 15 minutes, loosely covered with a tea towel or plastic wrap.
Using a floured rolling pin or your hands, stretch each ball into a 9-10-inch round (the shape doesn’t have to be perfect). Carefully lay one round of dough over the hottest part of the grill and cook until the bottom is lightly browned and dry, about 2 minutes. Using tongs, gently lift up the dough, flip over, and cook for just 30 seconds. Transfer to a baking sheet, with the less cooked side up, and repeat with the remaining dough rounds. Let cool.
Divide the sauce among the partially cooked pizzas and, using the back of a kitchen spoon, spread it evenly to within a half-inch of the edges of the dough. Divide the cheese among the pizzas.
Place one or two pizzas at a time on the cooler part of the grill and cook until the cheese is melted and the bottoms are crisp and golden brown, about 2 minutes. Transfer to a cutting board and drizzle with a little olive oil. Scatter six torn basil leaves over each pizza and sprinkle with coarse sea salt. Cut into slices with a pizza wheel and serve hot.