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

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

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

Add the Calabrian chili paste and stir for another minute.

Pour in the heavy cream and bring to a gentle simmer. Stir in the basil leaves and cook until wilted.

Blend the sauce until smooth, then return to the skillet. Stir in the Parmesan cheese until melted.

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.

Season with salt and black pepper to taste. Serve hot, garnished with additional Parmesan and fresh basil if desired.