1: Make the brine: Place the salt, the sugar, and 1 quart of warm water in a large stockpot or clean bucket and whisk until the salt dissolves. Whisk in 3 more quarts of cool water and the bay leaves, thyme, onion, and peppercorns.

2: Remove and discard the fat just inside the neck and body cavities of the goose. Remove the package of giblets, if any, and set it aside for another use. Rinse the goose, inside and out, under cold running water, then drain and blot it dry, inside and out, with paper towels. Place the goose in the stockpot with the brine. Place a heavy weight, like a saucepan or a large resealable plastic bag filled with ice, on top of the goose to keep it submerged. Brine the goose in the refrigerator for 24 hours.

3: Meanwhile, make the horseradish sauce: Finely grate the horseradish into a nonreactive mixing bowl. Add the mayonnaise, sour cream, if using, and lemon juice and whisk to mix. Season the horseradish sauce with salt and pepper to taste; the sauce should be highly seasoned. Set the horseradish sauce aside.

4: Drain the goose well, discarding the brine, and blot the goose dry with paper towels. For a more professional-looking presentation, truss the bird with butcher’s string following the instructions here.

5: To grill: If you are using the indirect method, this is best done on a charcoal grill. Set the grill up for indirect grilling, place a large drip pan in the center, and preheat the grill to medium. When ready to cook, if you are using a charcoal grill, toss 2 cups of the wood chips or chunks on the coals. If you are using a gas grill, add the wood chips or chunks to the smoker box or place them in a smoker pouch under the grate (see here). Place the goose, breast side up, in the center of the grate over the drip pan and away from the heat and cover the grill. If you are using a charcoal grill, you’ll need to add fresh coals to each side of the grill every hour and add 1½ cups of wood chips or chunks to the coals after the first and second hours.

If you are using a smoker, set it up following the manufacturer’s instructions and preheat it to 250°F. When ready to cook, place the goose in the smoker, breast side up.

6: Cook the goose until dark golden brown and cooked through, about 3 hours using the indirect method; 5 to 6 hours using a smoker, depending on the temperature outside. Goose breasts will take about 1 hour using the indirect method; 2 to 2½ hours in the smoker. Use an instant-read meat thermometer to test for doneness, inserting it into the thickest part of a thigh or breast but not so that it touches a bone. The internal temperature should be about 180 to 190°F. Another test for doneness is to pierce the side of the thigh or breast with a slender skewer; the juices should run clear.

7: Transfer the goose to a platter or cutting board and remove and discard the trussing string, if any. Let the goose rest for 10 to 15 minutes, loosely tented with aluminum foil. Carve the goose into slices and serve it with the horseradish sauce.