Cut the pork shoulder into 1-inch cubes, trimming any excess fat, then toss with the flour, salt, and pepper. Heat 2 tablespoons of oil in a skillet and brown the pork on all sides, then transfer to a slow cooker. You may need to work in batches and add a bit more oil until all of the pork is browned.
In the same skillet, saute the onion, peppers, garlic, adding a little more oil if the pan is dry, for 3 to 5 minutes. Add ½ cup of broth and scrape up any fond (the browned bits on the bottom of the pan) and transfer everything to the slow cooker with the pork.
In a blender, combine ½ the chopped tomatillos with ½ of the diced green chilies and the cilantro, then process until smooth. Add ½ cup of the chicken broth if necessary.
Pour the blended tomatillos into the crockpot and add all remaining ingredients except for the cornstarch and water. Cook on HIGH for 3-4 hours or on LOW for 6-8 hours until the pork is tender.
At this point, you can serve as is, or thicken by making a slurry with the cornstarch and water. Stir the slurry into the chili verde and cover again for 30 minutes, stirring occasionally, then serve in bowls garnished with lime wedges, cilantro leaves, green onions, sour cream, grated cheese, and tortilla chips or warm tortillas.