Pour the brown sugar sauce evenly over the sliced kielbasa in the slow cooker. Use a spatula or spoon to gently stir, making sure every piece is coated in the sweet, sticky mixture.
Cover the slow cooker with the lid and cook on LOW for 4 to 5 hours, or on HIGH for 2 to 2 1/2 hours, until the kielbasa is heated through and the sauce is bubbling and slightly thickened. Stir once or twice during cooking to keep everything well coated.
When the kielbasa is done, preheat your oven broiler to high and position a rack in the upper third of the oven. Give the kielbasa a final stir to coat it in the thickened glaze.
Using a slotted spoon, transfer the glazed kielbasa coins to the foil-lined baking sheet, spreading them out into a mostly single layer. Spoon a bit of the thick sauce from the slow cooker over the top of the sausage to encourage extra caramelized edges.
Place the baking sheet under the broiler for 3 to 6 minutes, watching closely, until the glaze darkens slightly, bubbles, and the edges of the kielbasa look sticky, glossy, and caramelized. Rotate the pan once if needed for even browning. Do not walk away; the sugar can go from perfect to burned quickly.
