Peel and slice the onions into 1/4 inch slices.
Melt butter and olive oil in a very large fry pan over medium high heat.
Add the onions.
Quickly cook the onions, moving them around the pan with a wooden spoon or spatula. It should take no more than 10 minutes for the onions to get nicely browned.
Adapted from: Joy of Cooking
Peel and slice the onions.
In a really large fry pan melt the butter and olive oil over really low heat.
Add the onions to the pan
Sprinkle on 1 teaspoon of salt.
Cook the onions over the lowest heat possible for about 1 hour.
Over the course of 1 hour they should not turn brown. Be sure to give them an occasional stir.
After about one hour increase the heat to medium and cook, stirring constantly, until the onions are well browned.
That could take another 25 minutes.
There will be a lot of brown bits stuck on the bottom of the pan.
Those bits are full of flavor.
To get them off the bottom of the pan and incorporated into the onions, pour 1/2 cup of dry white wine or water into the pan.
This will dissolve all the bits and make the onions even darker.
Add salt and ground pepper (Adjust to your taste).
Serve with parmesan cheese on the side.
Note: By the time you have finished caramelizing the onions they will have cooked down to about half their size.
Adapted from: Joy of Cooking