Step 1

Melt butter in a soup pot over medium heat. Add sausage and cook and stir until lightly browned, about 3 minutes. Use a slotted spoon to remove sausage to a bowl, leaving behind any butter in the pot.

Step 2

Toss onion into the pot with 1 teaspoon salt. Cook and stir until onion just starts to turn translucent and picks up a brown color from the meat juices in the pan, 4 to 5 minutes. Add flour; cook and stir for 2 to 3 minutes. Add garlic and paprika; cook and stir until fragrant, about 1 minute, being careful not to burn the paprika.

Step 3

Stir in 5 cups chicken broth. Increase heat to high and bring to a simmer, stirring occasionally so flour does not stick to the bottom of the pot. Stir in cabbage and cook until it just loses its stiffness, about 2 minutes. Stir in potatoes and bring back to a simmer. Add black pepper, cayenne pepper, and bay leaf, plus a splash of chicken broth if desired. Bring back to a simmer.

Step 4

Stir soup and reduce heat to medium-low. Simmer, stirring occasionally, until potatoes are very soft and tender, about 30 minutes. Add sausage and vinegar and simmer for 10 minutes. Taste and adjust for salt.

Step 5

Remove from heat and ladle into bowls. Garnish with sour cream, green onions, and cayenne pepper.