Heat the olive oil in a large Dutch oven or soup pot over medium-high heat. Add the sausage and cook for 5–7 minutes, breaking it into small pieces, until browned; drain excess fat if necessary.

Add the diced onion, carrots, and celery to the browned sausage. Cook for about 5 minutes, stirring occasionally, until the vegetables begin to soften.

Stir in the minced garlic and cook for 30–60 seconds, just until fragrant. Avoid letting the garlic brown, as it can become bitter.

Pour in the chicken broth and crushed tomatoes. Add the Italian seasoning, kosher salt, black pepper, and optional red-pepper flakes, then bring the soup to a boil.

Reduce the heat and simmer the soup uncovered for 15–20 minutes. This gives the vegetables time to become tender and allows the sausage, tomatoes, and herbs to develop a full flavor.

Stir in the refrigerated tortellini and cook according to the package directions, usually 3–7 minutes. Keep the soup at a gentle simmer and stir carefully so the pasta cooks evenly without breaking.

Add the baby spinach and cook for 1–2 minutes, until wilted. If using chopped kale, simmer it for several additional minutes until tender.

Taste the soup and adjust the seasoning with more salt or pepper if needed. Ladle into bowls and finish each serving with grated Parmesan.