Bring a large pot of water to a boil and generously season it with salt. Add the pasta and cook according to the package instructions. (Cavatappi usually cooks in 9 minutes).
While the pasta is cooking, pour the heavy cream into a large skillet. Add the cheddar, parmesan, salt, and pepper. Bring everything to a gentle simmer. Keep it over a very low heat until the pasta is cooked.
Drain the pasta, reserving some of the pasta water. Add the pasta to the cheesy sauce and mix well. Use pasta water to thin the sauce (I use about ¼ cup of water). Serve and enjoy!