Step 1

Heat broiler. Place oranges, cut side up, in a single layer on a rimmed baking sheet. Broil until flesh is charred, 7–9 minutes. Let sit until cool enough to handle.

Step 2

Juice oranges into a measuring glass to get 2 cups juice and pulp (add water to bring to correct volume if needed); set orange juice aside. Place juiced orange halves in a large Dutch oven or other heavy pot.

Step 3

Toast coriander seeds, cumin seeds, and dried oregano in a small skillet over medium heat, stirring often, until fragrant, about 2 minutes. Transfer to a blender and add garlic, chipotle chiles, honey, ¼ cup Diamond Crystal or 2 Tbsp. plus 2 tsp. Morton kosher salt, and ½ cup reserved orange juice. Blend on high speed until a mostly smooth paste forms (some texture is okay).

Step 4

Rub chile paste all over pork and set over oranges in pot. Pour remaining reserved 1½ cups orange juice around pork. Cover pot and chill at least 12 hours and up to 24 hours. Let pork sit at room temperature 30 minutes before roasting.

Step 5

Preheat oven to 325°. Roast pork, covered, 3½ hours. Uncover and continue roasting until meat is very tender and shreds easily with a fork, about 3 hours more. Transfer pork to a platter and let rest 20 minutes before shredding or slicing. You can toss the meat with some of the juices and liquid left in the pot if you would like; discard the rest.Do ahead: Pork can be roasted 5 days ahead. Cover and chill (in liquid), or freeze in a resealable plastic bag up to 1 month.