The day before cooking, remove neck and giblets from cavity of goose (use for stock if you like), as well as any lumps of fat. Rinse goose inside and out and pat dry with paper towels. Cut lower two joints from wings, leaving one joint (use lower joints for stock). Transfer to a rack set in a rimmed baking sheet. Prick goose skin all over with a small metal skewer or paring knife, angling skewer or knife sideways so you only prick skin, not meat. Season generously inside and out with salt and pepper. Chill overnight, uncovered.
Remove goose from refrigerator about 1 hour before roasting. Meanwhile, prep vegetables: Bring a large pot of water to a boil. Add onions and boil 1 minute. Lift out with a slotted spoon to a baking sheet to cool. To boiling water, add potatoes (keep whole so they're not waterlogged), 3 bay leaves, and about 1 tbsp. salt. When water returns to a boil, reduce heat and simmer potatoes until just tender, 15 to 20 minutes. Transfer to baking sheet with onions to cool.
Preheat oven to 450°, with one rack in lower third of oven and another in upper third. Pat goose dry and peel 2 or 3 onions. Stuff the onions, a few thyme branches, 2 bay leaves, and 2 apple quarters into goose cavity. Tie kitchen twine around body to hold wings close to body and tie ends of legs together. Set a V-shaped rack in a large (12- by 16-in.) roasting pan. Set goose in rack, breast up.
Roast goose 30 minutes. Carefully remove roasting pan from oven, lift goose in rack to a rimmed baking sheet, and pour accumulated fat from pan into a heatproof bowl. Reduce oven to 350° and return goose to roasting pan. Roast another 30 minutes, then pour off fat as before. Baste top of goose with 1 to 2 tbsp. fat. Continue roasting, checking temperature with an instant-read thermometer inserted in thigh joint every 30 minutes, until thermometer registers 170° to 175°, about 30 minutes more, pouring off fat if more than about 1 in. accumulates.
While goose roasts, peel remaining onions and scrape peels off potatoes with a spoon (easier than using a knife). Cut potatoes into quarters. In a large bowl, mix potatoes, onions, remaining apples, 6 or 7 branches thyme plus the minced thyme, 1 tsp. salt, and 1/2 tsp. pepper. Reserve 3 1/2 tbsp. fat and save the rest for another use.
Transfer goose on rack to rimmed baking sheet and tent loosely with foil. Increase oven to 500°. Oil two rimmed baking sheets with a bit of reserved goose fat, then drizzle vegetables with remaining fat and toss gently to coat. Spread vegetables on two rimmed baking sheets and roast until crisp and browned on edges, 15 to 20 minutes, stirring halfway through.
While vegetables roast, carve goose (see "How to Carve a Goose," below).
Drink pairing: A medium-bodied, silky red wine like Twomey 2013 Pinot Noir (Russian River Valley; $55). Layers of spice and loam set off rich red berry fruit.
*Marysturkeys.com raises Embden geese, a large white domestic goose bred especially for the table. Order directly from Mary's or Whole Foods Market.
How to Carve a Goose
A goose is built differently from a chicken or turkey, so carving takes a bit of time if you're new to it, plus it's somewhat messier. Our advice: Tell everyone to enjoy their wine while you carve the goose in the kitchen.
Lift goose, breast side down, to a cutting board. Snip off twine. Pour vegetables back onto baking sheets and keep warm in a 200° oven.
Remove wings: Slice under wing up to body, then grasp end of wing and push backward to pop joint loose. Cut through joint, then slice off meat. Set meat in frying pan over low heat, skin side down, to keep warm.
Remove breasts: Turn goose breast side up. Using long, gliding strokes, slice close to keel bone to release each breast half, bearing in mind that the bone tends to curve inward a little as you move downward, then flare out sideways. Transfer breast halves to pan, skin side down.
Remove legs: Cut legs free from thighs at the knee joint (similar to a chicken); set in pan. Keeping very close to bone, cut around thigh, turning goose over and slicing up toward center of back to loosen the "oyster," a nugget of meat. Grasp end of thigh bone and push back to pop joint loose. Cut through joint, then slice off meat and transfer to pan, skin side down.
Finish by cutting all remaining bits of meat and skin from bird (you will discover a long shoulder blade near the wing joint, called a "saber" bone; often there's more meat underneath) and adding to pan. As meat and skin crisp, transfer to platter.
Add vegetables back to platter. Garnish with thyme branches, sprinkle everything lightly with salt, and serve.