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