Preheat the oven's broiler and set the oven rack about 6 inches from the heat source. Toast muffin halves under broiler until golden, about 2 to 3 minutes. Mix garlic, butter, and basil together in a small bowl; spread butter mixture evenly onto each toasted muffin half.
Combine tomatoes, olives, and tomato paste in a large bowl; set aside. Whisk together the olive oil, lemon juice, and honey in a small bowl. Spoon some of the tomato mixture onto each muffin, then drizzle the olive oil mixture over the top, place a piece of mozzarella on top, and season with salt and pepper.
Return muffins to broiler; cook until the cheese has melted, 1 to 2 minutes. Serve immediately.