Preheat grill to medium-high. Place each pizza crust on a sheet of foil; set aside.
Heat olive oil in a small skillet over medium heat. Add garlic and onion; cook, stirring frequently, until onion is softened.
Brush pizza crust with olive oil mixture; arrange the onion, tomatoes, artichoke hearts, mushrooms and basil on crust. Sprinkle with cheese.
Grill pizza on foil sheets in covered grill for 5 to 7 minutes or until cheese is melted.