Preheat grill to medium.
Combine tomato, beans and corn in a medium bowl. Sprinkle cornmeal onto a large baking sheet. Stretch the dough into about a 12-inch circle and lay it on top of the cornmeal, coating the entire underside of the dough.
Transfer the crust from the baking sheet to the grill. Close the lid and cook until the crust is puffed and lightly browned on the bottom, 4 to 5 minutes.
Using a large spatula, flip the crust. Spread barbecue sauce on it and quickly sprinkle with the tomato mixture and cheese. Close the lid; grill until the cheese is melted and the bottom of the crust is browned, 4 to 5 minutes.
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