Preheat grill. Preheat oven to 400 degrees F.
Cut kielbasa into 3-inch lengths and butterfly lengthwise. Place on hot grill and cook for 4 to 5 minutes on each side turning frequently, charring all sides. Remove from grill. Transfer kielbasa to a baking sheet and place in oven to cook for another 5 to 6 minutes.
In a large skillet over medium-high heat, add butter and sugar. Allow sugar to cook to a golden brown color. Add onions and cook until caramelized. Stir in the sauerkraut and cook for 5 to 6 minutes until onions and sauerkraut are wilted and colored.
Remove kielbasa from oven and cut into 1-inch pieces. Add to pan of sauerkraut and onions. Toss together and cook for 1 minute. Transfer to a platter, garnish with parsley and serve with Honey Mustard Dipping Sauce.
In a small bowl, mix all ingredients until well combined.