Pat the beef chuck roast dry and season both sides with salt, black pepper, and a little chili powder.
Heat olive oil in a large skillet over medium-high heat. Sear the beef for 3–4 minutes per side, until browned.
Transfer the browned beef to a slow cooker.
In the same skillet, sauté the diced onion and bell pepper for 3–4 minutes.
Add the minced garlic and tomato paste. Cook for another 1 minute.
Transfer the vegetables to the slow cooker.
Add the diced tomatoes, tomato sauce, kidney beans, black beans, and beef broth.
Sprinkle in the chili powder, cumin, smoked paprika, oregano, salt, black pepper, and cayenne pepper.
Cover and cook on LOW for 8–9 hours or HIGH for 4–5 hours, until the beef is very tender.
Carefully remove the beef and shred it with two forks.
Return the shredded beef to the slow cooker and stir it into the chili.
Cover and cook for another 15–20 minutes to allow the shredded beef to absorb the sauce and seasonings.
Taste and adjust the seasoning before serving.