Heat gas grill to medium-low or charcoal grill until coals are ash white. Place coals to 1 side in charcoal grill.
Cut 1/2-inch slice off top of bread; set aside. Remove bread from center of loaf leaving sides and bottom of bread about 1/2-inch thick, using small knife. Set aside bread bowl and extra bread.
Place American cheese and garlic into food processor bowl fitted with metal blade; pulse until cheese is coarsely chopped. Add Parmesan cheese, milk, cream cheese and nutmeg. Pulse until well mixed. Spoon mixture into bread bowl.
Wrap bread bowl loosely in aluminum foil. Place opposite heat on grill. Close lid; grill 20-25 minutes or until cheese mixture is heated through.
Cut remaining bread into 1-inch pieces.
Stir cheese mixture before serving. Serve immediately with bread pieces and vegetables, if desired.
– Bread bowl can be filled, wrapped in aluminum foil and refrigerated up to 24 hours before grilling. Bring to room temperature before grilling.
– To bake in oven, heat oven to 350°F. Wrap bread in aluminum foil as directed. Bake 30 minutes. Open top of foil; fold back edges. Continue baking 10 minutes until cheese mixture is heated through and bread is slightly toasted. Stir cheese mixture before serving.