In a pan or cast iron large skillet, heat up a drizzle of olive oil. Add in your thinly sliced onions and season with salt. Let that sweat out and caramelize a bit on medium heat to medium-high heat for about 10-15 minutes, stirring occasionally.
About halfway through your onions, add in your balsamic vinegar, 2 tablespoons butter and red wine and reduce that down to finish caramelizing, about another 15-20 minutes. Season with salt and pepper. Set aside.
Take your rolls and cut them lengthwise so you have 2 slices (top and bottom) Place in an oven-safe prepared pan to fit the rolls.
Make your butter topping sauce and melt your remaining 2 tablespoons butter in a pot or microwave. Toss in chopped thyme and parsley.
Brush your butter mixture on the bottom buns. Then, add on your caramelized onions on top, then top with your shredded cheese and finish with a sprinkle of fresh thyme. Cover with the top buns.
Take a brush and brush over your melted butter and herb mixture on the top bun of the rolls.
Bake for 15-20 minutes until the butter has melted, the buns are toasted and the cheese has melted. Remove and serve!