Bring a large pot of salted water to a boil. Cook cavatappi according to package directions until al dente. Reserve 1 cup of pasta water, then drain and set aside.
In a small bowl, mix salt, garlic powder, onion powder, paprika, and pepper. Sprinkle the seasoning mixture evenly over the chicken pieces.
In a large skillet, heat olive oil and 1 tablespoon butter over medium-high heat. Once the butter has melted and the oil is shimmering, add chicken. Sear for 3–4 minutes per side, or until golden brown and cooked through to an internal temperature of 165°F. Transfer to a plate and cover loosely with aluminum foil.
Reduce heat to medium. To the same skillet, add the remaining butter and garlic and cook for 1 minute.
Stir in flour and cook for 1 more minute, stirring constantly to form a roux.
Slowly whisk in chicken broth and heavy cream. Bring to a simmer and let thicken for 3–4 minutes, stirring often.
Remove from heat. Stir in parmesan cheese and season to taste with salt and pepper.
Add the cooked pasta to the sauce and stir to coat. If the sauce is too thick, add reserved pasta water 1 tablespoon at a time as needed.
Top with the cooked chicken and toss to combine.
Garnish with fresh parsley and more parmesan. Serve hot.