Cook rigatoni in water with the tablespoon salt until 1 minute short of the package time. Reserve 1 cup pasta water before draining.
Meanwhile, rub thighs with paprika, garlic powder, onion powder, thyme, cayenne, chicken salt and pepper. Heat oil in a large skillet and cook for 5 to 7 minutes per side until browned and at least 165°F; transfer to a board to rest.
Lower heat and melt butter in the skillet. Add cream and milk, scrape up browned spice bits and simmer gently for 3 minutes.
Add rigatoni and 1/4 cup reserved pasta water and toss for 1 to 2 minutes. Remove from heat and stir in Parmesan, adding more water if needed for a smooth coating.
Slice rested chicken and serve over the pasta, spooning a little sauce around the meat.