Cut off the stem and root ends of the onions, then halve then lengthwise, and peel away the dried skin. Cut the onions into 1/4-inch slices. It is important to have all the onion slices roughly the same size so they cook evenly.
Stove Top: Melt butter in large soup kettle or Dutch oven over medium-high heat. Add sliced onions and 1/2 teaspoon salt, stirring to coat onions thoroughly with butter. Cook, stirring frequently, until onions are reduced and syrupy and inside of pot is coated with very deep brown crust, approximately 30 to 35 minutes.
Oven: You can also caramelize the onions in the oven. Please check out my article on Baked Caramelized Onions. This oven method cuts down on the cooking and stirring time required when you caramelize on your stove top.
Stir in chicken and beef broths, wine, parsley, thyme, and bay leaf, scraping pot bottom with wooden spoon to loosen browned bits; bring to simmer. Simmer to blend flavors, approximately 30 minutes. Remove herbs and discard. Stir in balsamic vinegar and adjust seasonings with salt and pepper to taste. At this point, the soup can be cooled to room temperature and refrigerated in an airtight container up to 2 days. To use, return to simmer before finishing soup with croutons and cheese.
Preheat oven to 400 degrees F. While the soup simmers, arrange the baguette slices in single layer on baking sheet and bake until the bread is dry, crisp, and golden at edges, about 10 minutes (watch carefully so they do not burn). Toasting the bread slows down the process of the bread getting soggy in the hot soup. Set aside until ready to use.
When ready to serve the onion soup, adjust oven rack to upper middle position; heat the broiler.
Set onion soup bowls on baking sheet and fill each with about 1 1/2 cups soup. Top each bowl with two (2) toasted baguette slices (do not overlap the bread) and divide Swiss cheese slices, laying them in a single layer on top of the bread.
I like to let the slices overlap the edge of the dish. It keeps the grated cheese from falling down into the soup, and looks cool when all brown and gooey. Remember, if you can see soup beneath, then you need more cheese.
Sprinkle the top of each with about 2 tablespoons grated Asiago cheese. Place the bowls into the oven, about 5 to 6 inches from the broiler and let broil until cheese is brown and bubbly, about 10 minutes.
Tip: For an onion soup not to collapse, the soup bowl has to be filled to the rim with the onion soup and the bread. The cheese layer should cover the whole surface, so it will stick to the sides and corm a crust that holds its shape and does not sink.
Remove from oven and serve immediately. Let your guests know that the soup is really hot!
Makes 6 servings.