Preheat the oven to 475 degrees F.

Remove the neck, giblets from the goose. Reserve the neck and giblets separately. Rinse the goose thoroughly inside and out under cold running water. Pat the goose dry with paper towels and season with the kosher salt and black pepper. Place the onions, carrots and celery in a medium bowl and toss to combine. Remove 1/2 cup of the vegetable mixture and set aside. Stuff the cavity of the goose with the remaining vegetable mixture, 2 bay leaves, 4 sprigs of thyme and 4 cloves of garlic. Truss the goose.

Using a fork, prick the skin of the goose on the thighs, back, and lower breast. Place the goose on a rack in a large roasting pan. Place in the oven and roast for 20 minutes. Reduce the oven temperature to 350 degrees F, pour 1/3 cup of hot water over the breast and legs of the goose and continue to roast the goose for another 30 minutes. Open the oven door and pour another 1/3 cup of hot water over the breast and legs of the goose. Close the oven and cook the goose another 30 minutes. Pour a final 1/3 cup of hot water over the goose to help the fat render from the bird and cook the goose until an instant read thermometer inserted into the thigh of the goose without touching the bone reads 165 degrees F, 30 minutes to 1 hour longer. Remove the goose from the oven and allow to rest.

While the goose roasts, prepare the goose stock. Use a heavy, sharp knife to chop the goose neck into 2 or 3 pieces. Place the chopped neck and giblets in a 2-quart saucepan and sear over medium heat. Cook the necks and giblets, turning occasionally, until well caramelized, 5 to 6 minutes. Add the reserved 1/2 cup of vegetables, the remaining bay leaf, sprig of thyme, 2 cloves of garlic, and 1/4 cup sliced shallots and continue to cook, stirring occasionally, until vegetables are wilted and lightly caramelized, 4 to 5 minutes. Add the stock, increase the heat to high, and bring to a boil. Reduce to a simmer and cook for 1 hour. After 1 hour, remove from the heat, strain through a fine-mesh sieve and reserve stock on the side. Discard solids. Pour the Armagnac over the blueberries and reserve separately.

Transfer the goose to a warmed platter, and pour off the fat that has collected in the roasting pan, (try to keep the browned bits on the bottom of the pan). Once most of the fat has been removed from the roasting pan, place it on the stovetop over medium heat over 2 burners. Add the minced shallots to the pan and cook for 1 minute, stirring with a wooden spoon to scrape up the browned bits. Add the Armagnac, blueberries, and thyme leaves and continue to cook until the Armagnac is nearly evaporated, about 1 minute. Add the reserved goose stock to the pan and reduce the heat to medium-low. Continue to cook until the stock is reduced by about half and the sauce is thickened, 4 to 5 minutes. Transfer to a sauce boat and serve alongside the goose.

Note: Be careful when basting the goose with water. The fat from the goose may splatter when the water drips down from basting.