Preheat the oven to 325 degrees F.
Mix the chili powder, salt, oregano and pepper together in a small bowl. Sprinkle the cubed pork chunks with the spice mixture and put into a large Dutch oven. Add 1 cup of the salsa verde, chicken broth, garlic and onions. Stir together with a wooden spoon. Put the pot on high heat and bring the mixture to a simmer. Transfer to the oven and cook, covered, until the pork is tender and easily shreds, about 1 hour 45 minutes. Once done, shred the pork in the Dutch oven with a pair of tongs or 2 forks.
Turn the oven up to 350 degrees F.
Combine the remaining 2 cups salsa verde and sour cream in a wide, medium bowl. Spread about 1/2 cup of the mixture on the bottom of a large rectangular casserole dish.
Wrap the tortillas up in a damp paper towel and microwave 40 seconds. Lay the warm tortillas out on your cutting board. Dip into the sour cream-salsa mixture and fill evenly with the shredded pork mixture and sprinkle of the cheese. Roll the enchilada up and place seam-side down in the baking dish. Pour the remaining sauce over the top and top with the rest of the cheese. Bake 30 minutes. Garnish with cilantro sprigs, if using.