In a 5 to 6 quart thick-bottomed pot, heat 3 tablespoons of olive oil on medium heat. Add the onions and toss to coat with the olive oil. Cook the onions, stirring often, until they have softened, about 15 to 20 minutes. Increase the heat to medium high. Add the remaining tablespoon of olive oil and the butter and cook, stirring often, until the onions start to brown, about 15 more minutes. Then sprinkle with sugar (to help with the caramelization) and 1 teaspoon of salt and continue to cook until the onions are well browned, about 10 to 15 more minutes.
Add the white wine to the pot and scrape up the browned bits on the bottom and sides of the pot, deglazing the pot as you go.
Add the stock, bay leaves, and thyme. Bring to a simmer, cover the pot and lower the heat to maintain a low simmer. Cook for about 30 minutes. Season to taste with more salt and add freshly ground black pepper. Discard the bay leaves. Add sherry, if using.
While the soup is simmering, line a sheet pan with parchment paper or foil and preheat the oven to 450°F with a rack in the upper third of the oven.
Brush both sides of the French bread or baguette slices lightly with olive oil (you’ll end up using about a tablespoon and a half of olive oil for this). Put in the oven and toast until lightly browned, about 5 to 7 minutes. Remove from oven.
Turn the toasts over and sprinkle with the grated Provolone cheese and Parmesan. Return to oven when it’s close to serving time and bake until the cheese is bubbly and lightly browned.
To serve, ladle soup into a bowl and transfer one cheesy toast onto the top of each bowl of soup.