Caramelized Onion and Horseradish Mashed Potatoes

1/4 cup light butter 4 cups chopped onions 2 teaspoons brown sugar 1 tablespoon white balsamic vinegar (optional) 2 1/2 lbs peeled and cubed baking potatoes[...]

3 tablespoons butter 4 onions , cut in half and sliced 1/2-inch thick 1 tablespoon white wine vinegar 1/2 teaspoon ground thyme 6 large baking potatoes ,[...]