Cider-Braised Pork Shoulder with Butternut Squash

Place pork shoulder on a rimmed baking sheet and rub all over with 3 Tbsp. salt. Let pork rest, uncovered, at least 1 hour and up to 2 to come up to room temperature. (This will help it to cook more evenly.)

Arrange racks in upper and lower thirds of oven; preheat to 300°. Slice squash in half lengthwise and use a spoon to scoop out seeds and stringy parts. Season all over with salt, then rub with a bit of oil. Transfer cut side down to another rimmed baking sheet.

Once pork is room temperature, pat dry thoroughly with paper towels. Heat 1 Tbsp. oil in a large Dutch oven over medium-high until shimmering and almost smoking. Cook pork on all sides until well browned, about 15 minutes total—be patient! Carefully transfer pork back to rimmed baking sheet, turn off heat, and even more carefully pour out whatever fat has accumulated in bottom of pot.

Return pot to medium-high heat and add apple cider, soy sauce, and ½ cup vinegar, scraping bottom to get up any crispy, stuck-on bits. Slice head of garlic in half crosswise and add to pot. Lower pork back into pot. Cover pork with a piece of aluminum foil and tuck it around pork. Cover pot and transfer to lower rack of oven. Place baking sheet with squash on top rack. Bake pork, turning after 1½ hours, until meat is very tender and pulling away from the bone, 3–3½ hours total. Bake squash until a fork poked through skin slides easily into flesh, 1–1½ hours.

Transfer pork to a large plate or platter, reserving pot with cooking liquid, and let rest until cool enough to handle—it’s a big piece of meat, so this will probably take close to an hour. Remove garlic with a slotted spoon and squeeze out cloves into braising liquid; discard skins. Tear pork into shaggy pieces, discarding any sections of fat or gristle, and return meat to pot with cooking liquid. Season pork and liquid with salt and a splash of vinegar. Slice scallions crosswise as thinly as possible.

To serve, reheat pork in liquid over low heat. Using a large spoon, scoop out pieces of squash and arrange on plates. Spoon pork and some juices over squash and garnish with sliced scallions. Serve with rice alongside.