Cut the onion in half, then into long slices. Add 1 tbsp butter to a large pan or cast iron skillet over medium heat. When the butter melts, add the onion. Let the onion cook for 3-4 minutes, stirring occasionally.
When the onions start to stick to the pan / brown, add 1-2 tbsp of water and continue to stir. This will deglaze the onions from the pan and add steam for the onions to continue to cook. After a few more minutes, add another splash of water. Repeat this process until the onions are golden brown and caramelized. This should take 10-15 minutes. Take the onions off the heat.
In a pan, add the remaining 1 tbsp of butter. Add one slice of bread, top with half the mozzarella, and a big scoop of the caramelized onions. Top with another slice of bread. Cook on both sides for a couple minutes until golden brown and until the cheese has melted.
If using, add red pepper jelly to each sandwich. Enjoy!