In a skillet, melt 1 tablespoon of unsalted butter over medium heat. Add the thinly sliced onion along with a pinch of salt. Stir frequently and cook for about 10 minutes until golden brown and soft. Stir in 1 tablespoon of balsamic vinegar and cook for another 2-3 minutes until coated. Remove the onions from the skillet and set aside.

In the same skillet, lower the heat slightly and add another tablespoon of butter. Lay two slices of sourdough bread in the skillet, and distribute half of the shredded sharp cheddar evenly on each. Layer the caramelized onions, followed by slices of medium apple and pear, then finish with the remaining cheddar on top. Place another slice of bread on each to complete the assembly.

Increase the heat to medium and grill the assembled sandwiches for about 4-5 minutes, checking for a golden brown crust. Carefully flip the sandwiches using a spatula, pressing down gently to ensure even grilling. Continue cooking for another 4-5 minutes until the cheese is melted and both sides are golden brown.

Remove the sandwiches from the skillet and let them cool slightly. Slice each sandwich in half diagonally to showcase the melted cheese and vibrant filling. Serve warm alongside a fresh salad or a bowl of comforting soup.