Warm 1/4 cup extra-virgin olive oil in a large saucepan over medium heat. Add 2 grated garlic cloves and cook until softened and light brown, 30 seconds to 1 minute.
Meanwhile, bring a large pot of salted water to a boil. Cook 1 pound fusilli pasta until al dente. Reserve 1/2 cup cooking water and drain.
Stir in 1/2 cup tomato paste until it darkens in color and fully incorporates with the oil. Cook for 2 to 4 minutes until simmering. Add 2 tablespoons vodka and continue stirring until it has evaporated.
Stir in 1 (14.5 ounce) can diced tomatoes and 2 cups heavy cream and reduce heat to medium-low. Season with 1/4 teaspoon salt and 1/8 teaspoon red pepper flakes.
When sauce is thick and smooth, add the cooked, drained pasta and 1 tablespoon butter. Toss to combine. If you need to loosen the sauce, add a couple of tablespoons of cooking water at a time until the right consistency is achieved. It should cling to the pasta, and look very smooth and glossy.
Divide between four bowls and top with Parmesan and basil. Add 1 ounce cubed, fresh mozzarella to each bowl if desired.
