Heat olive oil in a large pan over medium-high heat. Once olive oil is shimmering hot, sear chuck roast for 2 minutes on each side.
Place chuck roast (with oil and drippings from pan) in crock-pot. Add poblano pepper and sliced onion. Pour in beef broth and tomato paste. Add cumin, smoked paprika, oregano, and garlic. Stir ingredients. Place lid on crock-pot, and heat on low 6-8 hours.
Once beef is fork-tender, shred on a large plate, using two forks. Return to crock-pot for 30 minutes.
Serve over cauliflower rice with chopped onion, cilantro, and a lime wedge. Pan-fried plantain slices would also compliment this Cuban dish.