In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the short ribs and chorizo, cooking until browned on all sides. Remove from the pot and set aside.
In the same pot, add the diced onion, bell pepper, and garlic. Sauté for about 5 minutes, or until the vegetables are softened.
Stir in the chili powder, cumin, smoked paprika, oregano, salt, and black pepper. Cook for an additional minute to toast the spices.
Return the browned short ribs and chorizo to the pot. Add the diced tomatoes and beef broth, stirring to combine. Bring the mixture to a boil.
Reduce the heat to low, cover, and let simmer for 2 to 2.5 hours, or until the short ribs are tender and easily pull apart with a fork.
Once the short ribs are tender, remove them from the pot. Shred the meat and discard the bones. Return the shredded meat to the pot.
Stir in the kidney beans and black beans. Simmer for an additional 15-20 minutes to heat through.
Serve hot, garnished with fresh cilantro, and with sour cream and shredded cheese on the side.