Bring a large pot of salted water to a boil. Cook the cavatappi according to package instructions until al dente. Reserve 1 cup of pasta water, draining the rest. Set the cooked pasta and reserved pasta water aside.
To a large, deep skillet or Dutch oven over medium heat, add olive oil. Once hot and shimmering, add the ground beef, onion, and diced bell pepper. Cook, breaking the beef apart with a wooden spoon, until it is browned and the vegetables have softened (about 5–6 minutes). Drain excess grease if needed.
Add garlic and cook for one more minute.
Stir in hamburger seasoning, paprika, chili powder, salt, and pepper.
Stir in the diced tomatoes (with juices), corn, and heavy cream. Bring to a gentle simmer and cook for 5 minutes to let the flavors develop.
Reduce heat to low. Stir in the cheddar cheese and pepper jack until melted and smooth.
Add the cooked pasta to the skillet and stir until fully coated in the sauce. Add reserved pasta water, as needed, until the sauce reaches your desired consistency.
Garnish with parsley. Serve warm.