Cut the top and bottom off of each onion. Slice the onions lengthwise.
Heat the butter and oil in a large sauté pan over medium heat. Add the onions and coat with oil. Sauté slowly, stirring every 10 minutes or so. Cook 30–40 minutes, depending on how large the onions are and how dark you like them.
Deglaze the pan with your choice of liquid to add the flavor to the onions and lightly salt to taste.
One Last Thing
If you opt to use balsamic vinegar, the longer it has aged, the better and smoother it will taste!