In an electric stand mixer, combine 1 ¼ tsp active dry yeast, ½ tsp sugar and ¼ cup warm water that is about 95 to 110F. Stir until yeast is dissolved. Let sit for about 5 minutes or until mixture begins to foam.
Next, add 3 ½ cups of all-purpose flour, 2 tsp salt, ¼ cup olive oil, 1 cup room temperature water. Mix together all at once until the dough forms a ball.
Cover with plastic wrap and set in a warm place for the dough to rise for about an hour.
Punch the dough down and divide into smaller servings if desired. On a lightly floured surface, use a rolling pin to flatten each dough ball into as thin of a crust as possible. Transfer the dough to a pizza stone or cutting board for stability in moving it to the grill.
Heat grill to 400F. For a crispier crust, place the crust without toppings directly on the grill. Grill crust until browned, about 2 minutes.
Flip the crust. Add sauce, cheese and toppings. Reduce the heat to 250F and grill until cheese is melted. Serve hot and enjoy!