About an hour before you are ready to make the pizza, stir together the sauce ingredients in a medium bowl, and let the flavors blend at room temperature. Preheat one side of your grill to high (if your grill has a thermometer, have it between 500 and 600 degrees) and the other side to the lowest heat possible. Punch the dough down, divide it into four pieces, and let it rest on the counter and come to room temperature. Stretch the dough into four rounds (or ovals) of about 8 inches in diameter.

Brush two sheet pans with olive oil, and lay the rounds on the pans, flipping once so they are lightly oiled on both sides. Fish the garlic from the sauce, and discard. Depending on the size of your grill, you can make two or four pizzas at a time. Season the rounds lightly with salt. Slide the dough rounds from the sheet pans onto the hot side of the grill; it will stretch a little more as you transfer it, and that’s okay. Cook until the top blisters and bubbles and the bottom is cooked and charred in places, about 1 to 2 minutes, moving the dough occasionally if it seems to be cooking unevenly. Flip over to the cooler side of the grill with the bubbly side down. (A combination of tongs and a wide metal spatula are the best tools for this job.)

Quickly cover the pizza with sauce, then a thin layer of mozzarella. Add a few torn basil leaves, a dusting of grated Grana Padano, and a drizzle of olive oil. Cover the grill until the cheese begins to melt, about 1 minute. Lift the grill cover slightly to check on it, and lower the temperature if the dough is getting too charred. Open the grill, slide the pizza to the hot side, and cook until the underside is nicely charred, about 30 seconds to a minute more, moving the pizza around the grill as necessary to avoid burning. Using tongs, slide the pizza onto a cutting board, and serve.

Note: The dough for grilled pizza needs to be a little sturdier to transfer to the grill, so use less water.