Heat a large nonstick skillet or deep saucepan over medium heat. Add the sliced kielbasa and cook until nicely browned, stirring occasionally to ensure even coloring.

Once the sausage is seared, stir in the cubed potatoes, shredded cabbage, and chopped onion. Pour in the chicken broth along with 1/2 cup of water. Sprinkle in the sugar, caraway seeds, and black pepper, stirring to distribute the seasonings evenly.

Increase the heat and bring the mixture to a gentle boil. Once boiling, reduce the heat to low, cover with a lid, and simmer for 15 to 18 minutes. Stir occasionally to prevent sticking and to help the potatoes cook evenly until fork-tender.

Next, add the kidney beans and cider vinegar to the pot. Cover again and simmer for an additional 5 to 10 minutes, allowing the beans to warm through and the flavors to meld.

In a small bowl, whisk together the flour and the remaining 1/4 cup water until smooth and lump-free. Pour the flour mixture into the stew, stirring constantly. Bring the pot back to a boil, and cook for 2 minutes or until the stew thickens and has a velvety consistency. Serve warm.