Make the dough: Add flour to large bowl. Form a ‘well’ in the middle that is large enough to hold all the water.
Pour water into the well, then add sugar and yeast.
Form a ‘claw’ with your hand and use your fingers as a whisk. Slowly move your hand in a circular motion so the walls of the well don't fall down too fast. You just want a little bit of the flour incorporated at this stage, similar to a pancake batter.
Start incorporating more of the flour, whisking a bit more aggressively, eventually creating a very shaggy dough.
Evenly sprinkle salt on the dough and continue to incorporate the remaining flour until you have a thick dough and all the flour is incorporated.
Drizzle in the olive oil slowly and mix using your whole hand until the dough ball is semi-smooth and the oil is incorporated.
Turn the dough out onto a clean surface and continue kneading until the dough is well mixed and smooth. Form into a smooth round ball.
Resting/Proofing: Add 1 tablespoon olive oil to a medium size bowl. Place the dough (top side down) in bowl, coating with oil. Turn the dough over to coat rest of dough ball with oil. Cover bowl tightly with plastic wrap. Let dough rest for about 20 minutes at room temperature.
Remove the dough from the bowl and knead on counter for about 1 – 1½ minutes to incorporate the oil. Divide your dough ball into 2 or 3 equal portions, depending on the crust shape you desire, larger oval or round.
Gently pull the corners of the dough piece into a square, then bring the diagonal corners to the middle, and repeat with the opposite corners. Continue to bring the points into the center a few more times, then grab, pinch and rotate the seam like you’re closing a change purse, until the dough ball is smooth and tight. Repeat with remaining dough ball(s).
Place each dough ball in bowl. Do not coat with oil or flour. Cover with plastic wrap. Refrigerate the dough balls for 24 hours (or at least overnight, 8-12 hours).
Remove dough balls from the refrigerator 1 – 1½ hours before using, allowing dough to come to room temperature.
Preheat grill: Place pizza stone on one side of gas grill grate to allow air to circulate and also leaving space to grill the crusts. (See note)Or grill pizza dough first, and then preheat stone if grill is not big enough, or you are topping pizzas later. (Pizza stone size depends on the size of your dough and grill. We used a 14x14-inch stone in the video.) Preheat gas grill to 450°F. Shape Pizzas:Round crust (10-12 inches): Turn dough out onto a clean surface. Flatten and shape dough into a circle using your fingertips. Do not use a rolling pin! Press across the dough with your fingertips once it is shaped to ‘dock’ it. (See video for a no-fail shaping tip)Oval/rectangular crust (9x13 inches): First, spread a thin layer of olive oil on a ½ sheet baking pan or large cookie sheet; set aside. Place dough ball on a clean surface. Using your fingertips on both hands, ‘dimple’ across the dough on one side, then flip it over and ‘dimple’ the other side. Repeat. Lay dough onto the center of the baking sheet. Gently pull and dimple the dough out to almost the edges of the pan. With fingertips, press across the dough to ‘dock’ it.
Grill Crusts: Gently place dough directly on the grill (don’t add olive oil). Close grill lid. Cook 1 – 1½ minutes (lift with tongs to check for grill marks on the bottom). Flip over. Let cook for 30 – 45 seconds more (to char the bubbles). Place on cooling rack. (See note for make-ahead option) Add desired toppings then transfer to pre-heated stone with peel, close lid and cook until hot and desired crust color is achieved, about 6 – 8 minutes.