On a floured board, divide dough into 4 equal pieces; shape each into a ball. Roll out each ball into a 5- to 6-inch-wide round. Brush tops lightly with about half the olive oil. Place each round, oiled side down, on a 10- by 12-inch piece of foil (4 total). With your hands, flatten rounds to 1/8 inch thick and 7 to 8 inches wide. Lightly brush with remaining oil. Let stand, uncovered, at room temperature until slightly puffy, 15 to 25 minutes.
As dough stands, prepare barbecue for direct heat.
If using charcoal briquets, cover firegrate with a single, solid layer of ignited coals; let them burn down to desired heat. Set grill in place and measure heat.
If using a gas barbecue, turn all burners to high and close lid for 10 minutes. Adjust burners to desired heat. Set grill in place and measure heat.
When grill is medium (you can hold your hand at grill level only 4 to 5 seconds), lift 1 piece of foil and flip dough round over onto grill. Peel off and discard foil. Repeat to place remaining dough on grill, keeping rounds slightly apart. Cook until pizza crusts are golden brown on bottom, about 2 minutes.
With a wide spatula, transfer crusts to baking sheets, browned sides up. Cover crusts with topping choice and slide from baking sheet back onto grill. Cover barbecue with lid (open vents for charcoal), and cook until topping is hot and pizza bottoms are crisp and brown, 3 to 4 minutes. Remove from grill; add salt and pepper to taste.
Per pizza crust: 334 cal., 24% (81 cal.) from fat; 5 g protein; 9 g fat (8 g sat.); 54 g carbo (3 g fiber); 547 mg sodium; 7 mg chol.
Nectarine and Basil Toppings: For each pizza, thinly slice 1 small pitted firm-ripe nectarine (about 6 oz.) and mix with 1/2 teaspoon balsamic vinegar. Sprinkle pizza crust with 1/3 cup shredded jack cheese and 2 tablespoons finely shredded parmesan cheese. Lay nectarine over cheese. Top with 1 tablespoon pine nuts. When pizza is removed from grill, scatter with 2 tablespoons finely shredded fresh basil leaves.
Per pizza: 655 cal., 40% (261 cal.) from fat; 27 g protein; 29 g fat (11 g sat.); 75 g carbo (2 g fiber); 976 mg sodium; 55 mg chol.
Provençal Topping: For each pizza, spread 1/3 cup fresh chèvre (goat) cheese onto pizza crust; sprinkle with 1/4 teaspoon dried thyme. Lay 1/2 cup thinly sliced canned peeled red peppers on cheese and sprinkle with 2 tablespoons finely shredded parmesan cheese. When pizza is removed from grill, mound 1/2 cup salad mix on it.
Per pizza: 539 cal., 37% (198 cal.) from fat; 22 g protein; 22 g fat (11 g sat.); 63 g carbo (2 g fiber); 1,073 mg sodium; 36 mg chol.
Sausage-Gruyère Topping: For each pizza, sprinkle 1/3 cup shredded gruyère cheese and 2 tablespoons finely shredded parmesan cheese onto pizza crust. Lightly grate nutmeg over cheese. Thinly slice 1 cooked chicken-apple sausage (3 1/2 to 4 oz.) and lay meat on pizza crust.
Per pizza: 750 cal., 44% (333 cal.) from fat; 40 g protein; 37 g fat (15 g sat.); 62 g carbo (9 g fiber); 1,449 mg sodium; 69 mg chol.
Peking Duck Topping: For each pizza, spread 1 to 2 tablespoons hoisin sauce over pizza crust. Top with 1/2 cup shredded boned, skinned barbecued duck (from a Chinese market) or roast chicken and 2 tablespoons finely chopped green onion. When pizza is removed from grill, scatter with 2 tablespoons fresh cilantro leaves.
Per pizza: 548 cal., 28% (153 cal.) from fat; 25 g protein; 17 g fat (7 g sat.); 68 g carbo (7 g fiber); 1,068 mg sodium; 69 mg chol.
Margherita Topping: For each pizza, sprinkle 1/3 cup shredded mozzarella cheese over pizza crust. Top with 2 tablespoons finely shredded parmesan cheese and 1/2 cup chopped tomatoes. When pizza is removed from grill, scatter with small whole fresh basil leaves.
Per pizza: 517 cal., 37% (189 cal.) from fat; 22 g protein; 21 g fat (1 g sat.); 60 g carbo (9 g fiber); 922 mg sodium; 45 mg chol.