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.
Remove the tray from the oven and let the kielbasa rest for 5 minutes. The glaze will thicken further as it cools slightly, giving you that shiny, sticky finish.
Serve the brown sugar kielbasa warm straight from the foil-lined tray or transfer to a warm serving dish, scraping any extra glaze from the foil over the top. Offer toothpicks or small forks for easy potluck sharing.
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