Heat a large skillet oven medium heat and add olive oil. Toss in shredded brussels sprouts and garlic with salt and pepper, tossing to coat. Cook until wilted and golden, stirring occasionally, about 5-6 minutes. Remove sprouts from the skillet and place them in a bowl.

Heat the same skillet (or a separate griddle, etc) oven medium-low heat. Butter the outsides of every bread slice, then layer the sandwiches with slices of cheese, the brussel sprouts, a good drizzle of balsamic glaze and more cheese. Top off with a slice of bread, buttered-side up. Cook until each side is golden and crisp and cheese is melted, then gently flip and do the same.