Peel and thinly slice the onions from root to stem. There should be about 10 cups of sliced onions in total.

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 20 to 40 minutes. The amount of time will vary depending on your pot, stove, and onions.

Sprinkle with sugar to help with the caramelization and 1 teaspoon of salt. Continue to cook until the onions are well browned, about 10 to 15 more minutes.

Add the minced garlic and cook for a minute more.

Deglaze the pot with vermouth or wine

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 brandy if using.