Whisk olive oil, lemon juice, balsamic vinegar, garlic, shallot, 1/2 TSP salt, and 1/2 TSP pepper together in a large bowl. Add tomatoes and toss to combine. Set aside and let tomatoes marinade.
Cook pasta according to directions.
Meanwhile, places mozzarella cubes on a plate and put in the freeze for about 10 minutes, or until slightly firm.
Add pasta and mozzarella cubes to tomato mixture, tossing to combine. Stir in basil and add salt and pepper to taste. Serve immediately.