Peel the red onion and get the first layer of skin off.
Slice the onion
Pre-heat the pan and melt the butter, but don't make it too hot.
Put the onions in the pan and give them a good stir, make sure all rings are covered with the melted butter.
Turn up the heat a bit and keep stirring until the onion is nice and soft.
Now here is where the patience comes in, your onions are far from ready, turn the gas to the lowest you can get it on the smallest burner and put the lid on the sauce pan.
Keep it low and slow for about 25 minutes, give the onions a stir every 5 minutes.
After 25 minutes, put in the balsamic vinegar and stir the onions until they are all covered with the vinegar. put the lid back on and keep it cooking for about 5 to 10 minutes more.