Thinly slice the onions (doesn't need to be perfect.) Melt butter in a large Dutch oven or pot. Once melted, add the onions and sprinkle with salt and pepper.
Cook the onions over medium heat, stirring occasionally, until they are completely caramelized (about 45 minutes) Make sure to turn the heat down a bit if they start to burn.
Once the onions are caramelized, add the white wine and bring to a boil over high heat. Let the onions and wine boil for about 5 minutes, then add the beef broth. Season with salt and pepper.
Let the soup continue to simmer over medium-high heat for about 10 minutes, continuing to taste and adjust salt and pepper as needed.
Heat the broiler on high on your oven.
If you have oven-safe bowls, put soup into bowls and place lightly toasted bread on top of the soup. Top with shredded cheese. Place bowls on a rimmed baking sheet and place in the oven for 10 minutes or until cheese is properly melted from the broiler.
If you are not using oven-safe bowls, place lightly toasted bread on a rimmed baking sheet and top with cheese. Place in oven for 10 minutes or until cheese is melted from the broiler. Once done, carefully place cheesy bread on top of the bowled soup.