Bring a large pot of salted water to a boil. Add cavatelli pasta and cook according to package instructions until al dente.

Reserve 1 cup of pasta water, then drain the pasta in a colander.

In a skillet, heat olive oil over medium heat. Add minced garlic and sauté until fragrant, about 1 minute.

Stir in heavy cream and bring to a simmer. Add chopped basil and Calabrian chili paste, mixing well.

Add grated Parmesan cheese and stir until melted and creamy. Season with salt and pepper to taste.

Add the drained cavatelli to the sauce, tossing to coat. If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.

Serve immediately, garnished with extra basil and Parmesan if desired.