Grilling this dough gives it a flavorful char. To save time, it can be grilled and stored at room temperature overnight. Just top and bake.
Pour water into a large bowl. Sprinkle with yeast. Let stand until dissolved, about 5 minutes. Add 3 cups flour and 2 teaspoons salt, and stir until smooth. Add another 2 cups flour, and stir until smooth. Continue adding flour (up to 1/2 cup), 1 tablespoon at a time, stirring, until dough comes away from sides of bowl but is still sticky.
Turn dough out onto a lightly floured surface. Knead dough with floured hands: Throw it down on surface, pulling it toward you with 1 hand and pushing it away from you withthe other. Fold dough back over itself (use a dough scraper or awide knife to scrape dough from surface), and knead until smooth, elastic, and soft but still a little tacky, about 10 minutes.
Shape dough into a ball, and transfer to a lightly oiled bowl; turn to coat. Cover with plastic wrap, and let stand in a warm place until doubled in volume, about 3 hours.
Heat grill to high. Scrape dough out of bowl onto a lightly floured surface, and cut into 6 equal pieces. Shape each piece into a ball. Dust with flour, and cover with plastic wrap. Let stand until dough is almost doubled in volume, 20 to 30 minutes.
Holding top edge of 1 dough ball in both hands, let bottom edge touch surface (refrigerate remaining balls as you work). Carefully move hands aroundedge to form a circle, as if turning a wheel. Hold dough on back of your hand, letting its weight stretch it into a 12-inch round. Transfer dough to a lightly floured pizza peel (or an inverted baking sheet). Press out edges using your fingers. Lightly jerk peel; if dough sticks, lift, and dust more flour underneath.
Heat grill to high. Grill pizza dough, flipping occasionally, until charred and cooked through, about 4 minutes.
Dough balls can be refrigerated, wrapped in plastic, for up to 3 days, or frozen for up to 3 months. Bring to room temperature before using.