Heat 2 tablespoons of olive oil in a large skillet over medium heat. Add 2 large thinly sliced onions and a pinch of salt, stirring to coat. Cook for about 5-7 minutes until onions become translucent and soft.

Once onions are translucent, sprinkle in 1 tablespoon of brown sugar and 1 tablespoon of balsamic vinegar. Reduce the heat to low and stir frequently for 15-20 minutes until onions darken and reach a jam-like consistency.

Meanwhile, cook 6 to 8 slices of bacon in a separate skillet over medium heat until crispy, about 8-10 minutes. Transfer to a paper towel-lined plate.

Preheat a non-stick griddle or frying pan over medium-low heat.

Butter one side of each slice of sourdough bread with 1-2 tablespoons of butter in total. Layer cheese, caramelized onions, and crispy bacon on the unbuttered side of four slices. Top with another layer of cheese and cover with remaining slices of bread, buttered side up.

Grill each sandwich for about 3-4 minutes until bread is golden brown and cheese begins to melt. Flip to grill the other side.

Let sandwiches rest for about 1 minute before slicing in half. Serve warm.