Yes, pizza is not only possible but worthwhile as a waffle, with an extra-crisp ridged crust and little wells for sauce and cheese to run into. Your waffle maker does double duty as both an oven for the crust and a broiler for melting cheese.
Special equipment: Waffle iron (preferably large)
Stir together the tomatoes, 1 tablespoon olive oil, the salt, basil and garlic. Let sit at room temperature to give the flavors time to meld, about 1 hour.
Preheat a waffle iron to medium-high. Lightly dust a clean work surface with flour and roll out half of the pizza dough into a 6-inch round (or to the maximum size your waffle iron can fit). Brush one side with olive oil and place oiled-side down on the waffle iron, then brush the other side with oil. Close the iron (don’t push down) and cook until golden and cooked through, 4 to 6 minutes. Repeat with the remaining dough.
Meanwhile, heat the tomato sauce in a microwave until hot. Spread each pizza with half of the sauce and half of the mozzarella. Place one pizza back on the waffle iron and hold the top of the iron just over the cheese until melted, 1 to 2 minutes. Remove and garnish with basil leaves, drizzle with olive oil and sprinkle with Parmesan. Repeat with the second pizza.
Cut the pizzas into slices with a large knife or pizza cutter and serve.