Drizzle a non-stick pan with olive oil and heat over medium-high heat. Add the sliced onions and season with a dash of salt and black pepper. Cook for 5 minutes.
Add the balsamic vinegar to the onions and cook an additional 5 minutes.
Top two pieces of bread with cheddar cheese and top with the onions. Layer thin slices of apple over the onions and top with a slice of bread.
Butter the outside of both sides of the sandwich generously and add to the skillet. Cook each side on medium heat for 1-2 minutes, until the bread is golden brown and the cheese is melted.
Slice each sandwich in half and enjoy!