1.Heat the olive oil in a large skillet over medium-high heat. Sear the pork in the hot oil until browned on all sides, about 10 minutes. Place into a slow cooker along with the cumin, New Mexico chiles, quartered onion, garlic, and 1 minced jalapeno pepper. Pour in the water, cover, and cook on High for 6 to 8 hours, then reduce heat to Low and cook until the pork is tender and easily shredded, 12 to 16 hours more. Once cooked, remove the pork and vegetables to a large bowl and shred finely with two forks. Mix in enough cooking liquid to moisten the meat to your taste.
2.Prepare the pico de gallo 2 to 6 hours before the carnitas will be ready. Combine the tomatoes, onion, tomatillos, and 2 minced jalapeno peppers in a mixing bowl. Season with lime juice, salt, and pepper. Mix well, and refrigerate until ready to serve.
