Heat oil in a 6-quart Dutch oven over medium-high heat. Cook andouille, pepper and onion for 6 minutes until sausage edges brown and vegetables soften.
Stir in garlic, tomato paste, paprika, thyme, cayenne, pepper and salt for 1 minute.
Add broth and bring to a boil. Stir in cavatappi and simmer uncovered for 9 minutes, stirring frequently and adding reserved water if the pot becomes dry.
Fold in shrimp and cream and simmer gently for 4 to 5 minutes until shrimp reach 145°F and the pasta is tender; keep a little flowing sauce around the noodles.
Remove from the heat and stir in Parmesan. Rest for 2 minutes and divide among 5 bowls.