Heat olive oil in pan at medium heat and add sliced onion. Add salt.
Stir the onions every five minutes or so. Cook for about 20 minutes.
Add a small amount of balsamic vinegar to deglaze the pan.
Add red pepper and cook until softened.
Layer vegan cheddar, caramelized onion, and red pepper on a slice of bread. Top with other slice of bread.
Spread 1 teaspoon vegan mayo on the outside of one of the slices of bread. Place face down in a hot pan. While the grilled cheese is cooking over medium heat, spread the other teaspoon of vegan mayo on the other piece of bread (the side facing you). Cook until golden brown on both sides. Repeat with the other sandwich.