1. Start by caramelizing the onions. In a skillet over medium heat, melt 1 tablespoon of unsalted butter. Add the thinly sliced onions and a pinch of salt. Cook, stirring occasionally, for about 10 minutes until they are golden brown and softened. Add the balsamic vinegar and cook for an additional 2-3 minutes. Remove from the skillet and set aside.
2. In the same skillet, melt the remaining tablespoon of butter over medium heat.
3. While the butter is melting, layer the grilled cheese. On two slices of sourdough bread, layer half of the cheddar cheese, followed by an even distribution of caramelized onions, then the apple slices, followed by the pear slices. Top with the remaining cheddar cheese and cover with the other two slices of bread.
4. Once the skillet is ready, place one sandwich in the skillet. Grill on one side for about 4-5 minutes, or until golden brown. Carefully flip the sandwich using a spatula and grill the other side for another 4-5 minutes, ensuring the cheese melts thoroughly.
5. Repeat the grilling process for the second sandwich.
6. Once both sandwiches are done, remove from the skillet, let them cool for a minute, then slice in half and serve warm.