Bring a large pot of salted water to a rolling boil. Add the cavatelli pasta and cook according to package instructions until al dente, typically about 7-9 minutes. Reserve 1 cup of the pasta water and drain the cavatelli.

In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add minced garlic and sauté for about 1 minute until fragrant, being careful not to brown it.

Lower the heat to medium-low and slowly stir in 1 cup of heavy cream, mixing well with the sautéed garlic. Allow it to thicken slightly for about 2-3 minutes.

Gradually add ½ cup of grated Parmesan cheese, stirring continuously until melted and incorporated.

Add ¼ cup of chopped fresh basil and 2 tablespoons of Calabrian chili paste, folding into the sauce evenly.

Add the drained cavatelli to the sauce, tossing gently to coat. Use reserved pasta water to adjust the sauce's consistency as desired.

Season generously with salt and freshly ground black pepper to taste.

Keep the skillet on medium heat for an additional 2-3 minutes, stirring gently to heat through.

Transfer to a serving dish, garnish with extra basil leaves and chili flakes, and serve immediately.