Place all ingredients, from the poblano peppers to the dark chocolate into a blender. Blend until it becomes a smooth puree.
Pour about ⅓ of the mixture into the bottom of the crockpot or baking dish. Place the whole chuck steak into the crockpot/dish. Pour the remaining pepper puree on top of the meat, making sure not to leave any of the steak exposed.
Set the crockpot to high and allow it to cook for 6 hours or until the meat easily falls apart with a fork. If cooking in the oven, bake in a dutch oven or similar with a tight lid. Bake for approximately 3 hours at 325 degrees.
Remove the meat from the dish and shred with a fork. Generously spoon some of the pan sauce over the shredded beef. Drizzle the meat with juice from half of a lime, sprinkle chopped cilantro and queso fresco over the top to garnish.
Reserve the remaining pan sauce for dipping tacos, making Enchiladas or to serve as a sauce with other meats, rice, beans or veggies.
The Shredded Mexican Style Beef is great served in taco shells or tortillas with Sweet Corn Salsa and extra crumbled cheese. Or serve as an entree with a side of rice and beans.