Preheat the grill to high (500°F). Clean the grates.
Once the grill is up to heat, oil the grates with vegetable oil.
Begin by grilling the tomatoes, cut side down, for 5-7 minutes or until charred and softened. Flip them and grill on the skin side for 2-3 more minutes. Remove to a large bowl.
Being very careful because the tomatoes are hot, gently mash them with a potato masher. You want them to still be chunky but release some of their juice. Season liberally with salt and pepper. Taste for seasoning.
Using your fingertips, on a floured surface gently push the dough ball into a flat round. Lift the dough up and gently pull the disk wider and wider, making sure to keep it an even thickness. Do this until you have a round or rectangle shaped pizza pie that is ½ - ¼ inch thick through out.
Slide the pizza dough onto a floured pizza peel or on an upside down cookie sheet (lipped edge facing down). Gently slide the dough onto the heated grill, trying to keep its shape the best you can and grill on one side for 4-5 minutes or until puffed and lightly charred. Remove from grill.
Back on the countertop or work surface, flip the pizza over so the grilled side is facing up. Taking large spoonfuls of the mashed tomatoes, cover the pizza leaving some areas un-sauced. Next gently tear or cut the burrata and add the to the pizza. Finish with large torn pieces of basil, a sprinkling of salt and pepper and a little drizzle of olive oil.
Carefully slide the pizza back on to the pizza peel or cookie sheet and return to the grill. Grill for 5-6 minutes until the under side of the pizza is charred and the cheese has softened.
Remove and serve immediately with more fresh basil if desired.
Recipe Courtesy of Megan Mitchell
As Seen on Grill Next Door on Yahoo!