Cut ciabatta in half horizontally. Gently tear out center of loaf, leaving ½ to 1 inch of bread shell intact.
In a medium bowl, combine smoked mozzarella, whole-milk mozzarella, mayonnaise, and garlic salt. Press gently into hollow center of bread. Wrap with plastic wrap, and refrigerate for 1 hour or up to 8 hours.
Preheat grill to medium-high heat (approximately 350° to 400°). Remove plastic wrap, and place bread, cheese side up, on grill over indirect heat. Cook until cheese has melted, 4 to 7 minutes. Let sit for 5 minutes. Top with fresh basil. Cut into slices to serve.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/grilled-mozzarella-basil-ciabatta-recipe/