Dust work surface with flour. Roll pizza dough out to 15 to 16 inches. Sprinkle flour or cornmeal on a large un-rimmed baking sheet or pizza peel. Transfer the pizza dough to the baking sheet or peel.
Brush grill grate to clean it and oil it with an oil soaked paper towel. Slide the dough off the baking sheet or peel onto the grill and cook until it is firmed up and crisped on the bottom, 2 to 3 minutes.
Carefully, flip the dough over using the peel or tongs and baking sheet. Spread the pesto over the dough. Top with tomatoes and cheddar. Cover the grill and cook until the cheese is melted and the bottom of the crust is crispy, 5 to 7 minutes.