Cook pasta in salted water until al dente. Reserve 1 cup pasta water before draining.
Heat olive oil in a skillet over medium heat. Add minced garlic and cook until fragrant.
Stir in tomato paste and cook for 2 minutes.
Add vodka and simmer for 2 minutes to cook off alcohol.
Pour in heavy cream and red pepper flakes. Stir to combine.
Add cooked pasta to the sauce and toss to coat. Add pasta water if needed.
Season with salt and pepper. Sprinkle with Parmesan cheese.
Garnish with fresh basil leaves and serve hot.