The recipe I used (except I skipped the parchment paper and did use a rolling pin). I rolled out the dough, then placed on some floured aluminum pizza pans. It took some care to transfer from the pizza pan to the heated stone on the grill, but both pizzas made it (mostly) safely through the process. Parchment would have eased that process, but I didn't have any.
Ingredients
3/4 cups (6 ounces) lukewarm water
1/2 teaspoon sugar
1 package active-dry yeast
2 cups (10 ounces) unbleached all-purpose flour
1 1/2 teaspoons salt
Instructions
Combine the water and yeast in a mixing bowl, and stir to dissolve the yeast. Add the flour sugar and salt to the bowl and mix until you've formed a shaggy dough.
Turn the dough out onto a clean work surface along with any loose flour still in the bowl. Knead until all the flour is incorporated, and the dough is smooth and elastic, about 5 minutes. The dough should still feel moist and slightly tacky. If it's sticking to your hands and countertop like bubble gum, work in more flour, one tablespoon at a time, until it is smooth.
If you have time at this point, you can let the dough rise until you need it or until doubled in bulk (about an hour and a half). After rising, you can use the dough or refrigerate it for up to 3 days.
Cover the dough with the upside-down mixing bowl or a clean kitchen towel while you prepare the pizza toppings.
When ready to make the pizza, tear off 2 pieces of parchment paper roughly 12 inches wide. Divide the dough in 2 with a bench scraper. Working with one piece of the dough at a time, form it into a large disk with your hands and lay it on the parchment paper.
Work from the middle of the dough outwards, using the heel of your hand to gently press and stretch the dough until it's about a 1/4-inch thick or less. For an extra-thin crust, roll it with a rolling pin. If the dough starts to shrink back, let it rest for 5 minutes and then continue rolling.
The dough will stick to the parchment paper, making it easier for you to roll out, and the pizza is baked while still on the parchment. As it cooks, the dough will release from the parchment, and you can slide the paper out midway through cooking.