Brown sausage and onion in a 6-quart pot over medium-high heat for 8 to 10 minutes, breaking sausage into small crumbles and cooking it to 160°F. Drain all but 1 teaspoon of the rendered fat.
Stir in garlic for 30 seconds. Add broth and scrape up the browned bits from the bottom.
Bring to a simmer, add kale and pepper, and cook for 6 to 8 minutes until the leaves soften.
Add tortellini and simmer gently for the package time, 3 to 5 minutes, until tender.
Stir in lemon juice. Divide among 6 bowls and add the Parmesan evenly over each serving.