Heat the olive oil on medium high in a large non-stick skillet.
Add the sliced onions. Sauté, reducing heat as needed, until the onions begin to brown. About 15 minutes.
Season with a pinch of salt and pepper and add the agave or sugar. Toss to combine.
Reduce heat to medium low and continue to sauté until the onion are completely caramelized. About 15-20 more minutes.
Add the vegetable broth and thyme. Simmer until the broth has been absorbed, about 5-7 more minutes.
Remove the sprigs of thyme and let the mixture cool slightly.
This will make 4 sandwiches. Take two slices of bread spread the onion mixture on one side. Then if you are using some spreadable cheese, spread it on the other slice. Top the onions with vegan mozzarella.
Spread vegan butter on the outside of each slice of bread.
Heat a non-stick skillet on medium high, then place a sandwich in the skillet, brown on one side, flip and brown on the other side. Making sure the cheese is as melty as possible. Serve immediately. *