If using whole chiles, preheat oven to 300°. Break stems off chile pods, tear pods open a little, and pull out seeds. "Wear rubber gloves if you are not used to handling chiles," Malcolm advises, since chiles can cause a burning sensation. "A few seeds add more heat, but adding a lot of them can make the sauce crunchy."
Put chiles in a 4- to 6-qt. pot, rinse, and drain. Dry pot to use later.
Arrange damp chiles in a single layer on two baking sheets and toast in oven until fragrant, 3 to 5 minutes (they won't dry completely). Let cool, then break each chile into 2 or 3 pieces. "The time in the oven deepens the flavor, but the toasting probably goes back to cooks who had to grind the chiles by hand. Toasted pods are more brittle and easier to crush."
Make sauce: Warm oil in 6-qt. pot over medium heat. Add garlic and cook, stirring, 2 minutes. If using preground chiles, sprinkle over garlic, then gradually whisk in 3 1/2 cups water.
If using whole chiles, purée half of them in a blender with 1 1/2 cups water until you get a thick, velvety liquid with flecks of chile pulp, about 2 minutes. Pour into pot of garlic. Repeat with remaining pods and another 1 1/2 cups water. "Use 1 more cup of water to rinse out the blender, then pour it into the pot so you get all the good chile bits."
Stir in onion, chile pequin, oregano, and garlic salt. "The chile pequin, a hotter, smaller red chile, adds heat and texture to the sauce." Bring to a boil over medium heat, covered; then reduce heat, uncover, and simmer 20 to 30 minutes, stirring occasionally, until as thick as fudge sauce. Remove from heat and cool to room temperature. Stir in pork, making sure all pieces of meat are coated. Cover and chill overnight.
The next day, preheat oven to 300°. Bake, covered, until pork is fork-tender and sauce has cooked down, 2 3/4 to 3 1/4 hours. Stir halfway through. If the sauce looks watery after 3 1/4 hours, stir well again and cook uncovered for another 15 to 20 minutes. Taste and season with more garlic salt if you like.
Make ahead: Up to 1 week, chilled (add a bit of water to reheat in oven or on stove).
*Find ground Chimayó chiles (in limited supply) at santafeschoolofcooking.com ($25/4-oz. pkg.). Ordinary New Mexico chiles can be found at well-stocked grocery stores and Latino markets.