In a skillet, add the olive oil, balsamic vinegar and sugar. Add the sliced onions and heat them on low, stirring often, for 30 minutes to caramelize them.
While the onions are caramelizing, stir together the softened butter and Parmesan cheese. Spread the Parmesan butter on the insides of the bread. Butter the outsides of the bread for grilling.
Once the onions have caramelized, place them onto a plate and gently pat them dry. (You don’t want them to be too runny and make the bread soggy before grilling.)
Add a slice of Swiss cheese and some of the caramelized onions onto the buttered breads. Grill on a skillet or electric griddle. Flip carefully to prevent onions from sliding out!
Enjoy!