Cook the sausage and onion in a 4-quart heavy-bottomed pot over medium-high heat for 8–10 minutes. Crumble the sausage as it cooks. Once the onion is softened and the sausage is browned and cooked through, drain the excess grease. Pork or beef sausage should reach 160°F (71°C).
Add the garlic and cook for 1 minute. Stir in the flour and cook for 1–2 minutes. Add the basil, oregano, optional cayenne, hot sauce, mustard powder, black pepper, and red-pepper flakes.
Pour in the chicken broth, scraping the bottom of the pot. Slowly stir in the heavy cream. Bring the soup to a boil, then reduce it to a gentle simmer.
Add the kale and tortellini. Simmer for 3–5 minutes, or follow the tortellini package time if it requires longer. When necessary, add the pasta first and add the kale for the final 5 minutes.
Once the kale is tender and the tortellini has no firm or chalky center, taste the soup and add salt if needed. Serve immediately.