To caramelize the onions, first heat olive oil in a nonstick skillet over medium heat.
Add the sliced onions and cook for 25-30 minutes, stirring occasionally, until very soft and golden.
Add the apple cider and salt and bring to a simmer. Cook until the apple cider is reduced, about 5 minutes longer, then remove the onions from the heat.
In the meantime, to cook the bacon, add the strips to a skillet over medium heat and cook until browned, about 8-10 minutes.
Drain the bacon on a paper towel-lined plate.
Butter one side of each slice of bread, then stack with the buttered sides together.
Spread the unbuttered side with stone-ground mustard.
Add the Brie, then bacon, then onions, Gouda, and sliced apples to the sandwiches.
Add the sandwiches to a skillet over medium heat, putting them buttered-side down and topping them with the other slice of bread, buttered-side up.
Cook, flipping once, until both sides are golden brown, about 4-5 minutes.