Step 1Stir the yeast and sugar into the water and let the mixture stand until foamy, about 5 minutes.
Step 2Place the flour and salt in the work bowl of a food processor. Turn on the processor; slowly pour the yeast mixture through the feed tube and let the dough mass together. Next, add the oil through the feed tube and process the dough until it cleans the sides of the bowl but is still moist. If the dough is too sticky, add more flour; if too dry, add more water. When the dough is the right consistency--moist but not so wet that it sticks to your fingers or the sides of the bowl--process until kneaded, about 40 seconds. The dough should be supple and elastic when you stretch it with your hands.
Step 3Transfer the dough to a large plastic food bag, squeeze out the air and seal the top, leaving enough room inside for the dough to expand. Place the bag in a bowl and let it rise in a warm spot until doubled, about 1 hour. Punch the dough down. The dough can be used now or refrigerated up to five days.
Step 4Divide the dough into 4 equal portions (about 6 ounces each). Roll each piece on a floured board to make about an 8-inch circle. Stack the rounds between oiled sheets of wax paper. The dough can be rolled in advance and refrigerated several hours or frozen.
Step 1Prepare a hot fire one side of the grill; the grill rack should be 3 to 4 inches above the heat. Set up the cool side of the rack with the pizza dough and toppings. Alternatively, set up a small table nearby for your cool side.
Step 2Gently stretch 1 dough round into about a 9-inch circle; be careful not to stretch so that holes appear. If small holes appear, work around them and do not drizzle any oil or filling into these holes. Place the dough on a large, oiled, inverted baking sheet. Gently stretch the dough more if needed (it's easier right on the sheet).
Step 3When the grill is hot, use your fingertips to lift the dough by the two closest edges and carefully drape it onto the grill. Make sure the dough doesn't droop into the flame. The dough will puff slightly and grill marks will appear, about 1 to 2 minutes.
Step 4Use tongs to flip the crust immediately over onto the cool part of the grill. Quickly brush the grilled surface with 1 1/2 tablespoons of oil. Scatter 1/2 teaspoon of garlic, 1/2 cup of Fontina and 3 tablespoons of pecorino over the dough. Spoon dollops of tomato over the cheese; do not cover the surface, leave spots of cheese. Drizzle with 1/2 tablespoon of oil; lightly sprinkle with salt, pepper and red pepper flakes.
Step 5Slide the pizza back over the heat; use tongs to rotate it so the heat is even, cooking the pizza uniformly. Check the underside to be sure it's not burning. When the cheese is melted, about 4 minutes, remove the pizza from the grill.
Step 6To serve, sprinkle it with basil and thyme. Cut into easy-to-handle finger food servings. Serve warm. Repeat with the remaining dough and toppings.