Add 1 tablespoon olive oil to a medium-sized skillet and heat over medium-high heat. Cook and brown 4-5 pounds cubed boneless pork shoulder on all sides. Add the pork shoulder to the slow cooker.
In a food processor add 1 (28-ounce) can tomatillos and blend until smooth. Add it to the slow cooker along with ½ cup chopped onion, 2 teaspoons minced garlic , 1 (14-ounce) can green enchilada sauce, 1 (16-ounce) jar salsa verde, 1 (4-ounce) can diced green chilies, ½ tablespoon cumin, 1 teaspoon dried oregano, and 1 teaspoon salt.
Cook on LOW for 6 hours or HIGH for 4 hours. An hour before serving, take out 1 cup of juice from the slow cooker and whisk it with the cornstarch. Add it back to the slow cooker and allow it to cook and thicken for about 1 more hour.
Shred the pork using two forks and serve with tortillas or over rice!