1 bag uette, cut on the bias into 3/4-inch slices (2 slices per serving)
4 1/2 ounces Swiss cheese, sliced 1/16-inch thick
1 1/2 ounces grated Asiago cheese (about 3/4 cup)
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Let's Make It
1. Melt butter in large soup kettle or Dutch oven over medium-high heat; add sliced onions and salt. Stir 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, 30 to 35 minutes.
2. Stir in the chicken and beef broths, red wine, parsley, thyme, and bay leaf, scraping pot bottom with wooden spoon to loosen browned bits, and bring to simmer. Simmer to blend flavors, about 20 minutes, and discard herbs.
3. Stir in balsamic vinegar and adjust seasonings with salt and pepper. (Can be cooled to room temperature and refrigerated in airtight container up to 2 days); return to simmer before finishing soup with croutons and cheese). Remove and discard bay leaf.
4. For the Crusts: Adjust an oven rack to the upper-middle position and preheat oven to 350 degrees F. Spread the bread out on a rimmed baking sheet and bake, flipping once, until lightly browned, about 15 minutes. Remove the bread from the oven. Turn the oven to broil.
5. Set heat-safe soup bowls or crocks on rimmed baking sheet and fill each with about 1 1/2 cups soup. Top each bowl with two toasted baguette slices and divide Swiss cheese slices, laying them in a single layer, if possible, on bread. Sprinkle each serving with about 2 tablespoons grated Asiago cheese and broil until well browned and bubbly, 7 to 10 minutes. Cool 5 minutes and serve.