Cook onion in butter and oil in large pan. Use medium heat. Stir to break up onion rings. Continue to sauté the sweet onions until they are very soft. Stir periodically. This will take about 30 to 45 minutes. Raise heat to medium high and continue to sauté onions until they turn a deep golden brown. This will require close watching and frequent stirring as you want the onions to brown, not burn.
Slowly add beef broth, stirring and scraping bottom of pan to capture all flavors from browning the onions. Stir in sherry. Simmer partially covered, 30 to 40 minutes. Correct seasoning with fresh pepper. To serve, ladle hot soup into appropriate serving containers. Float a round crouton on top of each. Sprinkle each crouton with 1 T. Parmesan cheese. Cover with a slice of each of American and Swiss cheese, then top with a second tablespoon of Parmesan cheese. Put under broiler to melt cheese slices and brown Parmesan.
Testing Tips: The procedure for browning the onions may seem time consuming, but is well worth the effort. The caramelizing of the natural sugar in the onions is the key factor to the flavor in this soup. A better soup is achieved with homemade beef stock, unsalted, but you can get a good soup from canned broth. This soup can be made ahead then reheated. In fact, the flavor will be even better. It can also be served without the crouton and cheeses and is a wonderful soup to enjoy this way if you are dieting. Serves 6 to 8
Source: The Airporter Hotel and My Old Recipes