Preheat the oven to 400°F.
Remove the tomatoes from the vine, and slice the tops off of each. With a spoon, gently hollow out the centers of each tomato (leaving a ½-inch thick shell) and place in an empty baking dish. Set aside.
Drain any extra liquid from the tomato pulp, and then lightly chop the remaining pulp into smaller chunks. Place the chopped pulp into a medium-sized bowl.
In that same bowl with the tomato pulp, add in the bread crumbs, chopped basil leaves, shredded cheese, minced garlic, salt, and pepper. Drizzle with the melted butter and stir until fully combined.
With a spoon, gently fill the empty cavity of each tomato with the filling, until it is slightly overflowed. Drizzle the tops with olive oil.
Bake uncovered for 15 minutes, or until the tomatoes are soft and the cheese is melted. Serve warm.
