Slice onions so that they are thin, about 1/8 to 1/4-inch thick.

In a large skillet over medium-low heat, melt the butter and add the olive oil. Be sure to coat the bottom of the skillet.

Add the slice onions and sauté for 35 - 45 minutes depending on your desired doneness.

Just before removing from heat, add the tablespoon of chicken broth. This will deglaze the pan, removing that extra goodness from the bottom and adding it to your onions.