Place pork butt in 4- to 5-quart slow cooker; pour enchilada sauce over top. Cover and cook on Low for 8 to 10 hours (High: 4 to 5 hours). Remove butt and cut into 1-inch pieces.
Sauté onions in oil until tender and browned. Combine pork with onions, salsa verde, potatoes, and garlic in large saucepan or stockpot. Add enough of the enchilada sauce/pork broth from the slow cooker to make desired stew-like consistency.
Bring to a boil over medium heat. Reduce heat and simmer 15 minutes. Serve with dollop of sour cream and cilantro.