Wash salsify well and peel off the outer skin and coating. Cut into 2-inch pieces.
Heat oil in a large stockpot over medium. Cook sausage, stirring occasionally, until browned, about 10 minutes. Transfer to a plate. Add onion, beets and garlic to pot and cook, stirring frequently, until onions are tender, about 8 minutes.
Add rosemary, salt, black pepper and red pepper flakes. Stir in chicken stock, tomato sauce and reserved sausage. Bring to a boil, then reduce heat and simmer for 10 minutes; then add the salsify. Continue to simmer until flavors have melded and salsify is tender, about 15 minutes. Stir in spinach and season with salt and pepper.
Divide between four bowls and top soup with shaved cheese, if desired.