Heat oil in a large soup pot or Dutch oven over medium heat until shimmering. Add bacon and kielbasa and cook, stirring, until fat is rendering and bacon and sausage are browning in spots, about 5 minutes. Add onion and carrot and cook, stirring, until softened but not browned, about 4 minutes. Add cabbage and cook, stirring, until lightly wilted, about 3 minutes. Add sauerkraut with its juice, chicken stock, bay leaves, dill stems, and potato. Season to taste with salt.

Increase heat to high and bring soup to a boil. Reduce to a bare simmer and cook until potato is tender, about 10 minutes. Stir together cornstarch, paprika, and ½ teaspoon white pepper in a small bowl. Add 1 tablespoon (15ml) cold water and stir to form a slurry. Pour slurry into the soup and stir until evenly distributed. Return to a boil (soup should thicken very slightly). Season to taste with more salt and white pepper as desired. Stir in chopped dill and serve with bread.