“This is a grown-up braise—a company braise,” says Piper Davis, co-owner and cuisine director at Grand Central Bakery in Portland and Seattle. “It’s a technique more than a recipe.” The keys to that technique: cooking the meat in cider with one set of seasonings, straining and reducing the liquid, and then adding fresh vegetables toward the end. The cider’s acidity tenderizes the meat, and its sweetness balances the savoriness of the pork. “I don’t think anything goes better with pork than apples,” says Davis. “There’s a reason it’s a classic combination.”
Preheat oven to 300°. Season roast with 1 1/2 tsp. salt and 1 tsp. pepper. Heat oil in a 4- to 5-qt. dutch oven over high heat until very hot. Brown pork on all sides, turning as needed, about 10 minutes total.
Meanwhile, cut onion, medium carrots, and celery into 2-in. chunks. Arrange around the browned roast with garlic. Pour in 2 cups cider and 1 cup broth ("I make mine from the bones of Sunday night's chicken"), adding more of either if the liquid doesn't completely cover meat. Bring to a boil. Cover with foil, pressing it down onto meat to eliminate any air gaps, then add the lid.
Braise in oven 2 to 2 1/2 hours, until a fork slides right in; "it means the connective tissue has lost the battle and the muscle is loosening." Let cool, then chill overnight. (Or let sit until cool enough to handle.)
Preheat oven to 375°. Spoon off fat from roast and discard. Transfer roast to a plate. Remove twine and break roast into 2-in. chunks with your fingers. Strain braising liquid and return to pot (discard vegetables).
Reduce braising liquid to 2 cups over medium heat, 10 to 20 minutes. Return pork to pot. Taste and add more salt or pepper if you like. Cut rainbow carrots in half lengthwise and arrange over meat. Roast, uncovered, spooning juices over carrots a couple of times, until they begin to brown and are tender, about 50 minutes. "If it isn't browning up, feel free to pop it under the broiler."
Stir in thyme. Scatter parsley on top and serve with mashed potatoes.
*Find rainbow carrots at well-stocked grocery stores and farmers' markets, or use small orange carrots.
Make ahead: Through step 2, up to 2 days.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.