In a large skillet, melt 1/2 tablespoon of the butter over medium heat. Add the onions, stirring and cooking for 15 minutes.
In a small bowl, whisk together the balsamic vinegar and Dijon mustard. Set aside.
Stir in the brown sugar until fully coated. Stir in the vinegar mixture. Cover and reduce the heat. Cook for another 15-20 minutes, stirring occasionally. If the onions get too dry, add 1 tablespoon of vegetable broth. You may not need the whole amount of broth.
Remove from the heat and stir in the remaining 1/2 tablespoon of butter, salt and pepper. Garnish with chopped parsley. Serve hot.
If you've tried this recipe, come back and let us know how it was in the comments or ratings!