Thinly slice 3 pounds of yellow onions. Cook slowly, over low heat, in a large covered stockpot, with 6-8 T butter, 2 t salt, and 1/2 t sugar. As the onions sweat their liquids into the pot, slowly raise the heat to moderate, which will evaporate the liquid and help the onions brown. The more slowly the onions brown, the more complex their flavor; however, the longer they brown the more they will fall apart and the longer you will be waiting! I usually take about an hour to 1 1/2 hours for this part.
Once carmelized, slowly sprinkle in 3 T of flour into the onions, stirring all the while. Remove from heat. Blend in 4 HOT quarts of beef stock- stirring vigorously to remove any lumps from the flour. If liquid is not hot, flour will form lots of little lumps. Add 1 cup vermouth, salt and white pepper. Simmer 30-40 minutes.
I then toast the rounds and lay them on the soup when it has been ladled into the tureens:
I lay 4-5 slices of baby swiss cheese on each tureen and slide them under the broiler on high heat until browned and bubbling. Serve hot!