Preheat oven to 350 degrees F. Line a baking sheet with parchment paper.
In a large pan over medium low heat combine brown sugar, spicy brown mustard, apple cider vinegar, and black pepper. Whisk together over medium low heat until the sugar is dissolved.
Add the kielbasa pieces to the liquid and stir around until well coated.
Using a slotted spoon transfer the kielbasa pieces to the parchment paper-lined baking sheet.
Place in the oven and bake at 350 degrees F for 20 minutes.
After 15 minutes remove from ovenand carefully transfer the kielbasa pieces back to the sauce. Stir around to coat them again and using a slotted spoon transfer them back to the baking sheet.