In a large pot, cook the diced bacon over medium heat for 5 minutes until the fat renders and the bacon becomes crispy. Remove the bacon pieces with a slotted spoon and set aside.
Add the diced onion to the bacon fat remaining in the pot. Cook over medium heat for 5 minutes, stirring occasionally, until the onion becomes translucent.
Sprinkle the flour over the onion and stir well to coat. Cook over medium heat for 2 minutes.
Gradually pour in the broth or water, stirring constantly, until a creamy sauce forms.
Season the sauce with salt, pepper, and a splash of vinegar to taste.
Add the finely sliced white cabbage to the sauce and stir to combine.
Reduce heat to medium-low and simmer for 1 hour, stirring occasionally, until the cabbage is tender.
Taste the dish and adjust the seasoning with additional salt, pepper, or vinegar as needed.