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