Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it up with a wooden spoon, until no pink remains, about 5 minutes. Drain excess fat if needed.

Add the diced onion to the beef and cook until softened and translucent, about 4 minutes. Stir in the chili powder, cumin, and salt; cook for 30 seconds until fragrant.

Pour in the tomato sauce and Worcestershire sauce. Reduce heat to low and simmer, stirring occasionally, until thickened and flavors meld, about 15 minutes. The chili should be thick enough to cling to a spoon.

While the chili simmers, cook the hot dogs. Grill over medium heat for 4-5 minutes with occasional turns until charred in spots, or pan-fry in a dry skillet over medium heat until browned all over.

Split the buns and toast them cut-side down on the grill or in a dry skillet until golden and slightly crisp, about 1 minute.

Place a hot dog in each toasted bun. Spread a thin line of yellow mustard along the dog if desired. Ladle a generous scoop of hot chili over each dog, then sprinkle with shredded cheddar. Serve immediately while the cheese begins to melt.