Melt 1 tablespoon butter in a medium nonstick skillet over medium-high heat. Add onion and sugar; sauté 10 minutes or until caramelized. Remove from heat; stir in vinegar, if desired.
Place potato in a saucepan, and cover with water. Bring to a boil. Reduce heat; simmer 15 minutes or until tender.
Drain and return potato to pan. Add 3 tablespoons butter and milk; mash to desired consistency. Cook 2 minutes or until thoroughly heated, stirring constantly.
Combine Dijon mustard and remaining ingredients in a small bowl, stirring with a whisk until blended. Add Dijon mustard mixture and caramelized onion mixture to potato mixture, stirring to combine.