Heat a large skillet over medium-high heat. Add the ground beef and break it up with a wooden spoon into small crumbles. Cook for 7 to 9 minutes, stirring occasionally, until the beef is fully browned and no pink remains. Drain off all but about 1 tablespoon of the fat.

Push the beef to one side of the skillet and add the diced onion and bell pepper to the cleared space. Cook for 2 to 3 minutes, stirring the vegetables, until they begin to soften. Add the minced garlic and tomato paste and stir everything together. Cook for 1 more minute until the tomato paste darkens slightly and smells a little sweet and savory.

Sprinkle in the cumin, smoked paprika, chili powder, oregano, salt, black pepper, and cayenne if using. Stir to coat the beef and vegetables evenly in the spices and cook for 30 seconds so the spices bloom in the residual heat of the pan.

Transfer the beef mixture to the slow cooker. Add the drained black beans, crushed tomatoes, diced tomatoes with their juices, beef broth, and Worcestershire sauce. Stir everything together until well combined.

Place the lid on the slow cooker. Cook on LOW for 7 to 8 hours or on HIGH for 4 to 5 hours. The chili is done when it is thick, deeply colored, and the flavors have melded together. Taste and adjust salt as needed.

Ladle into bowls and top each serving with shredded cheddar and a spoonful of sour cream. Serve with warm cornbread, over white rice, or with tortilla chips on the side.