the potluck and the tray was licked clean

For a little heat to balance the sweetness, whisk 1 to 2 teaspoons of crushed red pepper flakes or your favorite hot sauce into the brown sugar mixture before pouring it over the kielbasa. If you prefer a deeper, molasses-like flavor, swap half of the light brown sugar for dark brown sugar. You can also use smoked kielbasa or a mix of kielbasa and another fully cooked sausage, such as andouille, for more complexity. To lean into a slightly tangier profile, replace half of the ketchup with barbecue sauce, keeping the total liquid amount the same so the glaze still thickens properly. If you need to stretch the recipe for a larger crowd, add up to 1 more pound of kielbasa and increase the brown sugar to 2 1/2 cups and the ketchup to 1 1/4 cups, keeping the mustard at 1/4 cup. Leftovers reheat well in a skillet over medium-low heat until the glaze loosens and turns glossy again; you can tuck them into rolls with a bit of sharp mustard for quick sandwiches.