Thinly slice the yellow onions.
Melt the butter and olive oil in a large pot over medium heat.
Add the sliced onions and season with salt and pepper.
Cook the onions, stirring occasionally, until very soft and caramelized, about 30-40 minutes.
Add the minced garlic (if using) and cook for 1 minute.
Deglaze the pot with the white wine and let it simmer until reduced by half.
Add the bone broth, miso paste, thyme sprigs, and bay leaf.
Bring the soup to a simmer and let it cook for 10-15 minutes.
Ladle the soup into bowls and top with toasted sourdough bread and grated cheese.
Garnish with extra fresh thyme.
