Set your oven to preheat at 350°F (175°C).
In a medium-sized mixing bowl, blend together the brown sugar, pineapple or apple juice, ketchup, soy sauce, Dijon mustard (if using), and garlic powder. Whisk until the mixture is smooth and well incorporated.
Arrange the sliced kielbasa evenly in a 9x13-inch baking dish. Pour the prepared glaze over the sausage pieces and mix thoroughly to ensure all slices are coated.
Place the baking dish, uncovered, into the preheated oven. Bake for 25 minutes, stirring once at the halfway point to help the glaze evenly coat and thicken over the kielbasa.
Remove the dish from the oven once the sauce has reduced and caramelized. Stir gently and transfer to a serving platter. Serve immediately with toothpicks for easy enjoyment.