To make the sauce: Prepare your outdoor grill for high direct heat. Brush both sides of each tomato half generously with olive oil and season with salt and pepper, then place them on the hot grill. Cook until the tomatoes are charred on both sides (about 6 minutes per side).

Let the tomatoes cool on a rimmed plate for 10 minutes, drain off any liquid and transfer the tomatoes to a food processor. Add the 1 tablespoon of oil, ¼ teaspoon salt, and the garlic. Pulse a few times, just until it looks like a chunky sauce. Taste and season with more salt and pepper if needed. Save ½ to ⅔ cup of the sauce in a ramekin for your pizza and pour the rest into an airtight container (you can use it for pasta later in the week).

To top and grill the pizza: Stretch or roll out the dough, brush it with olive oil, and grill one side for a few minutes, just until the dough puffs up a bit and has nice grill marks on the bottom. Remove the dough from the grill and flip it over onto a cutting board or pizza peel so the grill marks are on top. Spread about ½ cup sauce on your par-grilled crust and scatter on the cheese. Return the pizza to the grill and close the lid; cook for about 3 minutes, until the cheese melts, and then transfer it to a cutting board or platter. Garnish with the fresh basil, a drizzle of olive oil, and a pinch or two of salt and pepper before slicing and serving.

Note: If you want to make this pizza in your outdoor pizza oven, you can sear the tomatoes on a cast-iron grill pan to make the sauce. Top your stretched-out dough with the marinara and cheese, and bake at 700°F to 1,000°F until the crust is evenly cooked on the bottom and charred in spots around the edges.