Heat a dutch oven pot or a large soup pot to medium-high heat. Add the olive oil and butter. Once the butter is melted, add the onions and a pinch of salt and stir until onions have softened, about 5 mins. Once softened, turn down heat to medium low heat. Cook onions until caramelized, stirring every 5 minutes. This will take about 40-50 more minutes.
Add the sliced mushrooms and thyme, season with salt and pepper and cook for 5-7 minutes. Then add the wine and cook until the liquid has evaporated, about 3 minutes. Add the flour and stir for another 3 minutes.
Add the broth and let it simmer for 30 minutes.
Meanwhile, turn on your broiler and move your oven rack 5 inches away from the broiler. Toast your bread by placing them on a baking tray and letting them broil on that top rack, 5 minutes. Then grate each piece with a garlic clove.
Once the soup has reduced, stir in the miso making sure it’s well dissolved. Season with salt if needed.
To assemble, ladle the soup to oven-safe bowls, add the toasted bread and sprinkle with cheese. Turn the broiler on, place the bowls on a baking tray and position them on the same top rack. Broil until you get a nice cheesy crust on the toasts. This could take up to 5 minutes depending on how strong your broiler is.
Let the bowls cool a bit before serving and enjoy!