Step 1

Position racks in center and top third of oven; preheat to 400°F. Coat a broiler-safe 9-by-13-inch baking dish with cooking spray.

Step 2

Heat oil in a large pot over medium heat. Add kielbasa and cook, stirring occasionally, until crispy, about 2 minutes. Using a slotted spoon, transfer the kielbasa to one half of a paper-towel-lined plate (do not wipe out the pot).

Step 3

Add chicken to the pot and cook, stirring occasionally, until lightly browned but not completely cooked, about 4 minutes. With the slotted spoon, transfer the chicken to the other half of the plate with the kielbasa, reserving the drippings in the pot.

Step 4

Add cabbage and onion to the drippings in the pot; cook, stirring occasionally, until tender, about 5 minutes. Stir in sauerkraut, mustard, pepper and salt. Sprinkle with flour and cook, stirring constantly, until well incorporated, about 1 minute. Add milk and cook, stirring constantly and scraping to release any browned bits from the bottom of the pot, until simmering and thickened, about 4 minutes.

Step 5

Remove from heat and stir in 1 1/2 cups cheese. Stir in the chicken. Transfer to the prepared baking dish. Sprinkle with the kielbasa, breadcrumbs and the remaining 1/2 cup cheese. Bake on the center rack until bubbling and the chicken is completely cooked through, about 20 minutes. Turn the oven to broil and move the casserole to the top rack. Broil until browned on top, about 1 minute. Let stand for 5 minutes before serving.