Tie herb sprigs together with cotton twine; set aside.
Melt butter in a heavy stockpot over medium-high heat; add sliced onions and salt; stir to coat onions with butter.
As you cook the onions, gradually reduce heat to medium and keep cooking the onions, stirring occasionally, for 30 minutes or until the onions are reduced and syrupy and the inside of the pot is coated with a deep brown crust; stir in broth, wine, and herbs; scrape the pot bottom with a wooden spoon to loosen the browned onion bits as you bring the soup to a simmer.
Simmer for 20 minutes or until flavors are blended; discard herbs; stir in balsamic vinegar and add salt and pepper to taste ~ At this point, you may refrigerate the soup in an airtight container for up to 2 days, then return it to a simmer before finishing it.
To finish the soup, place your oven rack to the upper-middle position and turn on broiler; place heat-safe bowls on a rimmed baking sheet; fill each bowl with one cup of soup; top each with two baguette slices, sliced Swiss cheese, then 2 tablespoons grated Asiago cheese; place the baking sheet with its soup bowls under the broiler; broil until cheese is lightly browned and bubbly; cool 5 minutes then serve.
HINT: Slice the baguette on the bias so that two slices will fit your soup bowls.