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