Melt the butter in a large pot over low heat.

Add the thinly sliced onions to the pot.

Cook the onions, stirring occasionally, for 1 1/2 hours until they are deeply caramelized and softened.

Add the ground black pepper, salt, paprika, and bay leaf to the pot with the onions.

Stir in the all-purpose flour and cook for 10 minutes, stirring constantly, to create a roux.

Pour in the beef broth and white wine (if using) into the pot.

Simmer the soup over low heat for 2 hours, allowing the flavors to meld.

Adjust the color of the soup to a rich brown using the browning sauce.

Taste the soup and add more salt if needed.

Preheat your oven's broiler.

Ladle the soup into oven-proof bowls and place them on a baking sheet.

Float a slice of French bread in each bowl.

Top the bread with shredded Swiss cheese.

Broil the soup until the cheese is melted and browned.

Serve immediately.