Season pork pieces on all sides with salt and pepper.
Heat a large stock pot over high heat. Add oil. Once hot, sear the pork pieces until browned on all sides.
Remove the pork from the pot. Add a little additional oil to pan, if needed.
Reduce heat to medium-high, then add onion and saute until tender. Add garlic and cook for 30 seconds.
Stir in the cumin and oregano. Return the pork to the pot and add the chicken broth.
Reduce heat to medium-low, cover, and simmer for 3-4 hours.
Meanwhile, make the sauce.
Place rack on second to top level of oven and turn the oven to high broil.
Lightly spray a jelly roll pan with cooking oil. Wash all the peppers and tomatillos.
Slice the tomatillo and both types of peppers in half, and remove stems. Seed the peppers and remove the white veins inside if you do not want the chile verde to be very spicy. Do NOT seed the tomatillos.
Place the Poblano, Anaheim peppers, and tomatillos on baking sheets cut side down. Broil for about 7-10 minutes or until browned and wrinkled.
Immediately place peppers in a plastic bag zip-lock bag and seal. Allow them to steam for 5-7 minutes, and then peel off their outer layer of skin. (It should come off easily)
Add the peppers, tomatillos and cilantro to a blender and puree.
Add the mixture to the pot with the pork and cook everything together for an additional 30 to 45 minutes.