My grandmother-Rita- makes this soup after the holidays when there is leftover ham and a leftover ham bone. It is so delicious. Making the roux with the bacon fat really gives the soup the best flavor imaginable. However, if desired, you can make the roux with oil instead of bacon fat. This soup is delicious leftover too.
I have also made this soup with 2 ham steaks (with the small round bones in them) when I was craving it but did not have a ham bone leftover.
Place the bacon in a pan and cook over medium heat. Cook until crisp. Reserve bacon drippings.
In a large pot, cover the ham bone completely with cold water. Add the beans and the 1-2 cups leftover ham. Bring to a boil, then reduce to a simmer. Simmer, covered, for 1 hour.
Add the sliced cabbage and simmer, covered, for 30 minutes.
Add the cubed potatoes. Simmer, covered, until cabbage and potatoes are tender, about 20 to 30 minutes.
Remove the ham bone from the soup. Trim any remaining meat off the bone and dice it. Add the meat from the bone back to the soup. Discard the bone. Add the bacon to the soup.
Next, prepare the roux. Heat the reserved bacon fat in a pan over low heat. Add flour (enough to make the mixture stiff) and stir until smooth and thoroughly mixed. Cook, stirring constantly to prevent scorching. Cook until the roux is brown. Allow the roux to cool for a few minutes before adding it to the soup.
Add a small quantity of the roux to the soup and mix thoroughly. Let the roux simmer for a time to thicken completely. Continue to add the roux into the simmering soup until desired consistency is reached.
Season to taste with salt and pepper. Serve with warm, crusty bread.