In a large pot over medium heat, heat oil. Add onion and cook, stirring, until soft, about 5 minutes. Add chicken sausage and cook until golden, about 4 minutes, then add garlic and cook until fragrant, 1 minute more. Stir in crushed tomatoes, broth, and red pepper flakes and season generously with salt and pepper.
Bring to a boil and add tortellini. Reduce heat to medium-low and simmer until tortellini is cooked and flavors start to meld, 18 to 20 minutes.
Stir in white beans and spinach and cook until spinach has wilted, 2 minutes more.
Serve with Parmesan.