3 lb. pork butt or pork shoulder
1 tbsp. each ancho chile powder or chili powder blend, ground cumin, ground coriander, and dried oregano
¼ tsp. ground cloves
Kosher salt and coarsely ground black pepper
4 tbsp. neutral oil, such as safflower or canola, plus more as needed
1 large onion, sliced
1 large bay leaf
½ cinnamon stick
1 large orange, zest removed in large strips
½ can (6 oz.) lager beer, such as Modelo Especial
1 head garlic, cloves peeled and crushed
2 jalapeños, sliced
Hatch Chile Salsa
6 large fresh tomatillos, peeled, or 1 can (15 oz.) tomatillos
1 small onion, peeled and quartered
3 to 4 unpeeled garlic cloves
2 cups frozen mild, medium, or hot Hatch chiles (available online, in jars, or frozen in pouches), thawed, skins and seeds removed, if necessary
½ cup fresh cilantro or flat-leaf parsley leaves
1 tsp. dried oregano or 1 tbsp. fresh oregano leaves
1 tsp. light agave or mild honey
1 tsp. ground cumin
Juice of 1 lime
Charred soft corn or flour tortillas (heat over open gas flame or in a hot cast-iron or stainless skillet)
3 to 4 radishes, thinly sliced
Chopped white, sweet, or red onion tossed with lime juice, salt, and pepper
Sliced pickled jalapeños
For the carnitas, cut the pork into 2 1/2- to 3-inch chunks. In a large bowl, mix the spices. Add the pork and toss in the spice blend. Season the meat with 2 teaspoons salt and 1 teaspoon pepper.
In a large Dutch oven, heat 3 tablespoons oil, three turns of the pan, over medium. Add the pork and cook, turning often, until light to medium brown on all sides, about 6 minutes. Transfer to a large plate.
Add 1 tablespoon oil to the Dutch oven. Add the onion, bay leaf, and cinnamon stick; season. Cook, stirring often, until the onion is slightly softened, about 6 minutes. Juice the orange and 2 of the limes; add juices to the Dutch oven, scraping to loosen browned bits. Add the beer, garlic, jalapeños, and orange zest. Return pork to the Dutch oven. Bring to a simmer over medium-high. Cover and cook over low for 2 hours, turning pork halfway through. Uncover, add 1 cup of water, and continue to cook, turning pork occasionally, until the meat is fork-tender and the sauce thickens, 30 minutes to 1 hour more, adding more water halfway through if liquid gets too low.
Arrange a rack in the middle of the oven and preheat the broiler to high. Transfer the meat to a large plate, then remove the orange zest, bay leaf, and cinnamon stick. Using forks, shred the pork, then toss it with the sauce. Transfer the pork to a large rimmed baking sheet lined with foil, spreading the pork in an even layer. Broil the meat until slightly crispy on top and at the edges of the pan. Transfer the meat to a large shallow dish.
For the salsa, arrange a rack in the top third of the oven. On a large rimmed baking sheet lined with foil, arrange the tomatillos, onion, and garlic. Broil, turning the baking sheet occasionally, until the tomatillos and onions are charred and blistered, 10 to 15 minutes. When cool enough to handle, peel the garlic. In a food processor, blend the Hatch chiles, tomatillos, onion, garlic, cilantro, oregano, honey, cumin, and lime juice until it reaches the desired consistency for salsa. Season with salt and transfer to a bowl.
Wrap charred tortillas in a cloth napkin to keep them warm. Cut the remaining lime into wedges. Serve the carnitas with the tortillas, radishes, cilantro, seasoned onions, pickled jalapeños, and lime wedges.