Heat the oven to 400 degrees. Spread the tomatoes on a baking sheet large enough to hold them in a single layer. Add the garlic cloves. Sprinkle over the olive oil and season with salt.
Roast the tomatoes until they begin to wrinkle and caramelize, and their juices release into the oil, about 25 minutes. Remove from the oven and let cool completely.
Cut the mozzarella into 1/8-inch-thick slices and arrange, overlapping slightly, on a platter. Spoon the tomatoes and — most importantly — their juices and the oil, over the mozzarella. Season with salt and pepper. Drop the basil leaves on top. Enjoy!