Peel the onions and slice them thinly from root to tip, yielding about 10 cups of onions. Set them aside
In a large, thick-bottomed pot (about 5 to 6 quarts), warm 3 tablespoons of olive oil over medium heat. Toss in the sliced onions and stir well, ensuring they are evenly coated with the oil.
Cook the onions, stirring frequently, for about 15 to 20 minutes until they begin to soften.
Increase the heat to medium-high, add the remaining tablespoon of olive oil along with the butter, and continue cooking. Stir frequently until the onions start to caramelize, which should take anywhere from 20 to 40 minutes, depending on your stovetop and pot.
Sprinkle the onions with sugar and 1 teaspoon of kosher salt. Keep cooking until they reach a rich, deep brown color, stirring occasionally for another 10 to 15 minutes.
Stir in the minced garlic and cook for an additional minute.
Pour the wine or vermouth into the pot to deglaze, scraping the bottom and sides to lift any flavorful browned bits.
Add the stock, thyme, and bay leaves. Bring the mixture to a simmer, cover the pot, and reduce the heat to keep a low simmer. Let it cook gently for about 30 minutes.
After the soup has simmered, adjust the seasoning with salt and pepper to your taste. Remove and discard the bay leaves. Stir in the brandy, if using.
While the soup finishes cooking, preheat your oven to 450°F and line a baking sheet with parchment or foil.
Lightly brush both sides of the bread slices with olive oil (around 1 1/2 tablespoons of oil in total). Place them on the baking sheet and toast in the oven until golden, about 5 to 7 minutes.
Once toasted, flip the bread over and generously sprinkle the tops with the grated Gruyere and Parmesan cheese. Return to the oven shortly before serving to melt and brown the cheese.
To serve, ladle the soup into bowls and place a slice of the cheesy toast on top.
For an alternative method, use individual oven-proof bowls or a large casserole dish. Ladle the soup into the dishes, top with the toasted bread, and cover with the grated cheese. Place under the broiler at 350°F for about 10 minutes or until the cheese is bubbly and golden brown.
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