Evenly sprinkle salt, pepper and paprika over chicken drumsticks. Add 2 tablespoons to large saute pan over medium high heat. Once hot, add chicken and brown on each side for 5 minutes each. Remove from pan (keep warm).
Add remaining oil to pan, along with garlic. Let cook for 2 minutes, then add roasted red peppers and cook another 3 minutes. Next add broth, cream and parmesan. Bring just to a bubble and reduce heat to medium.
Stir 1 teaspoon of thyme and cayenne to sauce. Return chicken to pan and cover with lid. Let cook another 20 minutes.
Add pasta to boiling water and cook as directed on the package. Drain in colander and return to pot (away from heat). Add butter and remaining thyme and toss with tongs to coat noodles with butter.
Serve a portion of buttered pasta with ladle of sauce and piece of chicken. Garnish with more parmesan cheese, if desired