Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil.

Halve Anaheim chile peppers lengthwise; remove the stem, seeds, and ribs. Place peppers cut-side down onto the prepared baking sheet.

Cook in the preheated broiler until peppers are blackened and blistered, 5 to 8 minutes. Transfer to a bowl and over tightly with plastic wrap. Let peppers steam as they cool, about 20 minutes. Remove and discard skins; chop flesh.

Season pork with salt and black pepper.

Heat bacon fat in a large skillet over medium-high heat. Add pork; cook until browned, about 3 minutes per side.

Transfer pork to a slow cooker. Pour in beef broth and coat pork with tomato paste. Add roasted chile pepper, onion, red bell pepper, yellow bell pepper, lime juice, garlic, cumin, oregano, chili powder, cayenne pepper, and bay leaf.

Cook on Low until pork is tender, about 8 hours. Shred pork using 2 forks. Serve with avocados, cilantro, and lime wedges.