Heat oil in 5-quart Dutch oven over medium. Cook kielbasa and onion 6 minutes until sausage edges brown and onion softens.
Stir in garlic 30 seconds; add broth and cream. Gently simmer.
Add tortellini; cover and gently simmer 4 minutes. Uncover; carefully stir, adding reserved water only if bottom dries.
Add spinach and pepper; cook uncovered 2 to 3 minutes until filling hot, pasta tender, and spinach wilted. Follow any longer package minimum cooking time.
Remove from heat; fold in Parmesan. Rest 2 minutes until sauce coats pasta; divide among 4 bowls.