Preheat grill to 400-degrees F.
Combine the extra virgin olive oil and minced garlic in a small bowl.
Brush the olive oil and garlic mixture on each piece of the Naan bread.
Top with the sliced tomatoes and then on top of those, top with 2-3 slices of fresh mozzarella on each piece of Naan.
Place the Naan bread on the grill and grill until the mozzarella begins to melt (about 3 minutes), and bottom of the Naan has grill marks.
Remove from grill, and top with fresh basil leaves and serve.