Season pork with salt and pepper. Heat 1 tablespoon oil in a large frying pan over medium-high heat. Brown pork pieces in the hot oil, about 5 minutes. Place pork into the bottom of a slow cooker.

Heat 1 tablespoon oil in the same pan over medium-high heat. Saute onion, chopped Anaheim chile, and garlic for 5 minutes, adding more oil if needed. Add mixture to the slow cooker; pour in chicken broth.

Cover and cook on High until pork is tender and easily shredded with a fork, about 4 hours.

Set an oven rack about 6 inches from the heat source and preheat the oven's broiler. Brush the whole chile peppers with oil and place on a baking sheet.

Broil in the preheated oven for 5 minutes per side. Remove from the oven and let cool slightly, about 5 minutes.

Remove pulp and seeds from chiles and cut into pieces. Place into the bowl of a food processor with enchilada sauce, cilantro, cumin, and chili powder. Puree until smooth. Refrigerate until ready to use.

Remove pork from the slow cooker and shred using 2 forks; return to the slow cooker. Add pureed chile pepper mixture and stir well. Cook on Low, 3 to 4 hours more.