In a pot, let butter and oil melt (pay attention not to burn them).
Add onion slices and give a stir. Keep at medium heat.
IMPORTANT: in order to make them caramelize, youdon't have to keep stirring! You just have to let them brown on the bottom then stir, let brown and stir and so on.
Caramelization takes about 25 minutes. Adjust heat if necessary.If they seem burnt, reduce heat.
Deglaze (read post to see what this means) using balsamic vinegar (for alcoholic substitution, please read the post).
Add vegetable stock to the pan, also add sage leaves, bay leaf, salt and pepper and lower the heat at minimum.
Let simmer for about 20 minutes.
Turn on the broiler at 250° C (480° F).
Pour the soup into two cocottes, add one/two slices of baguette and two slices of cheese (or grated) on top.
Bake until cheese is bubbly and slightly golden brown.
If you don't have cocottes: place baguette and cheese on a baking tray, and let melt using broiler. Then put the bread slices on top of your soup.
P.S. YES, you can enjoy your French onion soup without cheese:)