Adjust oven rack to lower-middle position and preheat oven to 400°F. Spray a large Dutch oven with nonstick cooking spray.
Place the olive oil and butter in the pot and add the garlic and onions. Sprinkle with 1 teaspoon kosher salt and stir well. Cook, covered, for 1 hour until the onions have reduced in volume and have softened.
2 tablespoons olive oil, 4 tablespoons unsalted butter, 1 clove garlic, 3 pounds yellow onions, 1 pound sweet yellow onions, 1¾ teaspoons kosher salt
Remove the pot from the oven and stir, scraping the bottom and sides of the pan. Place the pot back into the oven and this time cover it with the lid left slightly ajar. Continue cooking the onions another 1 hour, and then give them another stir, scraping the bottom and sides of the pot. Return the pot to the oven, lid slightly ajar, and cook another 20-45 minutes or until the onions have completely softened and are golden brown.
Carefully remove the pot from the oven and place it on the stove over medium-high heat.
Cook the onions, stirring and scraping down the sides and bottom of the pot often, until the liquid evaporates and onions brown, 15-20 minutes. Reduce the heat to medium if the onions are browning too quickly. (Be careful NOT to burn the onions - the soup will be bitter.)
Continue cooking and stirring until the bottom of the pot has a dark coating, then stir in ¼ cup chicken broth, scraping the pot bottom and sides to deglaze the pot. Cook until the water evaporates and a dark crust coats the bottom of the pot, about 6-8 minutes. Add another ¼ cup of broth to deglaze the pot once again. Repeat the process twice more or until the onions are very dark in color.
8 cups low sodium chicken broth
Stir in the wine and the sherry and cook, stirring often, until the liquid has evaporated, about 3-5 minutes.
¼ cup dry white wine, ½ cup dry sherry
Add the remaining broth, thyme, bay leaves, freshly ground black pepper, ¾ teaspoon salt, and stir well. Scrape the sides and bottom of the pot to release any bits of browned bits of food. Increase heat to high and bring to a low boil.
4 sprigs fresh thyme, 2 bay leaves, ½ teaspoon freshly ground black pepper
Stir and reduce heat to low, cover, and simmer 30 minutes.
Remove the thyme stems and bay leaves and season with salt and pepper, if needed.