Cook the Pasta: Bring a large pot of salted water to a boil and cook the cavatappi pasta according to package instructions until al dente. Drain and set aside.
Make the Roux: Melt butter in a large saucepan over medium heat; whisk in flour and cook 2 minutes until smooth paste forms.
Add Dairy: Slowly whisk in heavy cream and whole milk, about 1/4 cup at a time, cooking 2-3 minutes until thickened.
Season the Sauce: Stir in dijon mustard, paprika, garlic powder, salt, and pepper; adjust seasonings to taste.
Melt the Cheese: Reduce heat to low, gradually add American cheese, medium cheddar, and half the sharp cheddar, stirring constantly until smooth.
Combine with Pasta: Stir cooked pasta into cheese sauce to coat evenly and pour into baking dish.
Top & Bake: Sprinkle with remaining sharp cheddar cheese. Broil 2-3 minutes until cheese melts or bake at 350°F for 12-15 minutes.
Serve: Serve immediately for creamiest texture; optionally garnish with dried parsley or extra paprika.