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. Remove from heat and set aside.
02 - Butter one side of each bread slice. Place 4 slices, buttered side down, on a clean work surface. If desired, spread a thin layer of Dijon mustard on the unbuttered side of the remaining 4 slices.
03 - Layer each bottom bread slice with 1 slice of cheddar, arrange a few slices of pear and apple, distribute a spoonful of caramelized onions, and top with another cheddar slice. Place the prepared bread slices on top, buttered side facing outward.
04 - Heat a skillet or griddle over medium-low heat. Cook sandwiches until bread turns golden brown and cheese melts completely, approximately 4-5 minutes per side. Press gently with a spatula during cooking for even browning.
05 - Slice each sandwich diagonally in half. Garnish with fresh thyme leaves if using. Serve immediately while hot and crispy.