In a large saucepan or dutch oven, heat the olive oil over medium heat.
Add the sliced onions and salt, stirring to coat them in the oil. Cook for about 10 minutes, stirring frequently until the onions become soft.
Sprinkle the sugar over the onions and continue to cook for an additional 20-25 minutes, stirring occasionally, until they are deeply caramelized and golden brown.
Add the minced garlic and cook for 1-2 minutes, until fragrant.
Stir in the dried thyme, bay leaf, vegetable broth, white wine (if using), soy sauce, and balsamic vinegar. Bring the stew to a gentle simmer.
Allow the stew to simmer for 20 minutes to meld the flavors. Taste and adjust the seasoning with black pepper as desired.
Remove the bay leaf before serving.
If desired, toast the crusty bread, and top it with vegan cheese, melting it under the broiler for a few minutes.
Serve a generous portion of the stew in bowls topped with the toasted bread and cheese.