Cut the chuck roast into 1-inch cubes. Blot the pieces thoroughly with paper towels so the exterior is dry enough to brown effectively.
Combine the Stubb’s Bar-B-Q spice rub, smoked paprika, cumin, onion powder, garlic powder, and dried oregano in a small bowl.
Coat the beef pieces evenly and generously with the seasoning mixture, ensuring that the spices cover all sides.
Allow the seasoned beef to remain at room temperature for 30 minutes while the vegetables are prepared.
While the beef rests, mince the garlic, cut the sweet yellow onions into approximately 1/2-inch pieces, and finely chop the seeded bell pepper into roughly 1/4-inch pieces.
Pour the vegetable oil into a large skillet and heat it over medium-high heat until the oil begins to shimmer.
Sear the seasoned beef in batches, leaving sufficient space between the pieces. Cook for approximately 3 minutes on each side, or until a deeply browned crust forms.
Avoid overcrowding the skillet, as cooking the meat in smaller batches encourages stronger browning and develops a richer savory flavor.
Transfer each batch of browned beef to a plate and reserve.
Using the same skillet and the flavorful fat remaining from the beef, add the chopped onions and bell pepper.
Cook over medium heat for 5–7 minutes, stirring periodically, until the vegetables have softened and the onions appear slightly translucent.
During the final minute, add the minced garlic. Stir continuously so the garlic releases its aroma without scorching.
Cooking the vegetables in the same skillet builds the chili’s flavor base while incorporating the browned beef drippings.
Transfer the sautéed onion, pepper, and garlic mixture to the slow cooker.
Add the drained kidney beans, the diced tomatoes together with their juices, and the beef broth.
Season the mixture with the salt and freshly ground black pepper, then stir until evenly combined.
Arrange the seared beef pieces in the chili mixture, gently pressing them beneath the liquid as much as possible.
Cover the slow cooker and cook the chili on the LOW setting for 8 hours.
When finished, the chuck roast should be extremely tender and separate easily when pulled with a fork.
Carefully lift the beef pieces from the slow cooker with tongs or a slotted spoon and transfer them to a cutting board.
Using two forks, pull the tender beef apart into bite-sized shreds.
Return the shredded meat to the slow cooker and stir it thoroughly into the chili so it can absorb the surrounding sauce.
Approximately 10 minutes before serving, grill the hot dogs over medium-high heat for 3–4 minutes. Turn them periodically until they are heated completely through and have developed light charring on the exterior.
Place the buns on the grill and toast them for approximately 1–2 minutes, just until warmed and lightly golden.
Keep the finished chili hot in the slow cooker while the hot dogs and buns are prepared.
Set one grilled hot dog inside each toasted bun.
Spoon a generous portion of the hot shredded-beef chili over each hot dog, allowing some of the flavorful sauce to settle into the bun.
Finish each serving with a spoonful of sour cream, shredded cheddar cheese, and fresh cilantro if desired.
Serve immediately while the hot dogs, buns, and chili are warm.