Add olive oil to a hot pan. Add sliced onion and cook on medium heat for about 35-40 minutes, or until onions are caramelized. Add balsamic vinegar to deglaze the pan.
Add sliced mushroom and tamari, and cook until mushrooms are tender.
Place vegan Swiss cheese on bread. Broil or toast 3-5 minutes, until cheese is melted*.
Spoon caramelized onions and mushrooms on top of vegan Swiss.
You could also assemble sandwiches and cook them in a pan on medium high heat on both sides until the bread is golden brown. I prefer broiling the vegan cheese first, and then making the sandwiches because that way it is a little less messy.