Rough chop onions so that slices are between ⅛ and ¼ inches thick.
Heat the butter and olive oil in a saucepan on medium heat. Once the butter has melted, add onions and sweat them until they become translucent.
Reduce heat to low and continue to cook onions, stirring every 5-10 minutes to prevent them from sticking. Deglaze pan with a tablespoon or two of water or chicken stock when fond starts to form on the pan.
As onions continue to caramelize, continue stirring every 5-10 minutes and deglazing the saucepan as fond forms and the onions are no longer loose in the pan.
When the onions achieve a blonde color they are perfect for cooking French Onion Soup.
When the onions achieve a golden-brown or caramel color they are perfect for making French Onion Dip.
When the onions achieve a deep golden-brown (or dark brown) they are perfect as a pizza or burger topping.