01 - Heat olive oil in a large skillet over medium heat. Add sliced onion and pinch of salt. Cook, stirring frequently, until soft and golden brown, about 15 minutes. Stir in balsamic vinegar and cook 1–2 minutes more. Set aside.
02 - Butter one side of each bread slice. Place 4 slices, buttered side down, on a clean work surface.
03 - Layer each bread slice with 1 slice of cheddar, a few slices of pear and apple, a spoonful of caramelized onions, and another slice of cheddar. If desired, spread a thin layer of Dijon mustard on the inside of the top bread slice.
04 - Top with remaining bread slices, buttered side up, to complete the sandwich assembly.
05 - Heat a skillet or griddle over medium-low heat. Cook sandwiches until bread is golden brown and cheese is melted, about 4–5 minutes per side. Press gently with a spatula for even browning.
06 - Slice sandwiches in half, sprinkle with fresh thyme if desired, and serve warm.