Heat the oil in a large skillet or saucepan over medium heat. Add the diced onion and sauté for 3–4 minutes, until softened and slightly translucent.
Add the ground beef and cook for 5–7 minutes, breaking it apart with a spatula, until browned and fully cooked.
Stir in the tomato paste, paprika, salt, garlic powder, cumin, and cayenne pepper. Cook for 1 minute, stirring frequently, until the tomato paste and spices are well incorporated.
Add the tomato sauce, beef broth, and Worcestershire sauce. Stir everything together and bring to a gentle simmer.
Simmer uncovered for 15 minutes, stirring occasionally, until the chili thickens. If it becomes too thick, add a small splash of beef broth.
While the chili is simmering, cook the hot dogs using your preferred method.
Lightly toast the hot dog buns until warm and golden.
Place each cooked hot dog inside a toasted bun. Spoon the homemade chili generously over the top, then sprinkle with shredded cheese.
Place the assembled chili cheese dogs on a baking sheet and broil for 1–2 minutes, watching closely, until the cheese is melted.
Serve immediately and enjoy!