Gently warm olive oil in a spacious pot over medium-low heat. Add the thinly sliced onions along with a sprinkle of salt, letting them soften slowly and release their natural sweetness. Cook slowly for 35–45 minutes, stirring frequently, until onions are soft and golden brown.

Stir in minced garlic, thyme, and bay leaf. Cook for 1–2 minutes until fragrant.

Add white wine (if using) to lift the brown bits and deepen the flavor. Allow the mixture to simmer gently, letting the liquid cook down until it's reduced by half.

Pour in vegetable broth, tamari, and nutritional yeast or miso paste. Raise the heat to bring it to a boil, then reduce to a gentle simmer. Let cook for 20–30 minutes. Season with salt and pepper to taste.

While the soup simmers, toast the bread slices until golden. Top with vegan cheese and broil until melted and bubbly.

Ladle hot soup into bowls. Top each bowl with a cheesy toast slice. Garnish with fresh thyme if desired.