In a large pot or Dutch oven, heat the olive oil and vegan butter over medium heat. Add the sliced onions and cook, stirring frequently, until caramelized and golden brown, about 35 - 40 minutes. If onions begin to scorch, lower the heat slightly.
Add minced garlic, and stir for one minute until fragrant.
Evenly sprinkle the flour over the onions. Stir well mixed for about 1 minut to coat the onions and cook out the raw flour taste..
Pour in the balsamic vinegar and add 1/4 cup of vegetable broth. Use a wooden spoon to actively scrape up all the delicious browned bits (fond) stuck to the bottom of the pot, to deglaze.
In a small bowl, whisk the miso and another 1/4 vegetable broth until smooth with no lumps. Pour this mixture, the remaining vegetable broth, tamari, thyme, rosemary, and salt into the pot. Add the bay leaf.
Bring the soup to a boil, then reduce the heat to low, cover, and simmer for an additional 30 minutes to allow the flavors to meld together.
Turn on your oven brolier. Remove and discard the bay leaf. Ladle the hot soup into oven-safe bowls. Top each bowl with 1 or 2 slices of your hard-toasted baguette, then generously layer the vegan cheese over the top of the bread.
Place the bowls of soup under the broiler and broil until the cheese is melted and bubbly, about 2-3 minutes. Watch carefully.
Remove carefully. Serve hot.