Begin by making the onion jam, so you can chill it for about 1 hour before making the sandwiches (if you don't have that much time, you can also put it in the freezer for about 25 minutes, after completed, to cool it down).
Start by placing the butter in a nonstick pot (medium sized) over medium heat.
Melt butter, and then add in onions and salt. Toss to coat them in butter, for about 1 minute, to make sure they are all evenly coated.
Cover and let cook for 5 minutes until onions start to slightly brown.
Then add in 1 cup of water and mix well. Cover and let cook for 15-20 more minutes, until onions have cooked down and are extremely soft, and the mixture has thickened.
Once cooked down, add in brown sugar, red wine vinegar, and balsamic vinegar. Mix well and keep mixing. Don't stop so the mixture doesn't burn. Keep mixing for about 5-6 minutes until the mixture is thickened and jam-like.
Once thickened, remove from heat. Place into a glass or metal airtight container and place in fridge to chill for about 60 minutes.(This can also be made the day before and kept in the fridge overnight.)