Preheat oven to 425°F and line a large sheet pan with parchment paper.
Add peppers, garlic, onion, sauerkraut, and potatoes to the pan. Drizzle with olive oil, salt, and pepper. Toss to coat.
Bake 15-18 minutes, or until the vegetables are tender.
While the vegetables are cooking, slice the kielbasa into ¼-inch slices, but not all the way through. Place the kielbasa between two chopsticks or skewers. (These will prevent you from cutting through the kielbasa completely.) Using a sharp knife, slice in a downward motion, stopping at the chopsticks.
Remove the sheet pan from the oven. Toss the veggies and nestle the kielbasa into them.
In a small bowl, combine mustard, apple cider vinegar, brown sugar, and Worcestershire sauce. Brush about ⅓ of the mixture over the kielbasa, reserving the rest for basting.
Transfer the pan back to the oven and bake for 40-45 minutes, or until the potatoes are fork-tender, basting with the mustard mixture every 10 minutes.
Garnish with parsley. Serve warm.