Heat the oil in a heavy-bottom Dutch oven over medium-high heat. Cut the chuck eye roast into 2-inch pieces and place in the Dutch oven to brown on all sides. Transfer the browned beef to a plate with a slotted spoon, leaving any juices in the pot. Reduce the heat to medium and add the onion and green pepper. Cook for about 2 to 3 minutes, and then add the garlic. Stir to combine and be careful not to burn the garlic. Add the chili powder, oregano, cocoa, sugar, 1 teaspoon salt, and 1/4 teaspoon pepper. Stir well to combine. Add the beef stock, scraping the bottom of the Dutch oven to pull up all of the flavorful bits on the bottom. Work the tomato paste into the vegetables and beef stock until dissolved. Add the crushed tomatoes, apple cider vinegar, Worcestershire sauce, and the reserved beef with the juices back to the pot. Combine well, bring to a boil, and reduce to a simmer, cover and let cook for 2 hours.
After 2 hours, remove the large beef chunks from the chili and shred with 2 forks. Return the beef back to the pot with the beans and cook, covered, for an additional 1/2 hour. Serve with shredded cheese, sour cream, hot sauce, chopped onion, or guacamole.
Cook's Note: This is chunky and flavorful chili made from tender shredded beef with the perfect amount of heat. I use a homemade blend of ground dried chile peppers including ancho, chipotle, and pasilla. I also slow cook and shred a chuck eye roast as opposed to using traditional ground beef.