Heat 2 tablespoons oil in Dutch oven over medium heat; add ½ cup onion. Cook until onion is tender. Add beef; cook and stir for 5 minutes. Stir in chili seasoning, Worcestershire sauce, chili paste, tomato sauce and beef broth. Bring to boiling; reduce heat and simmer, stirring occasionally until thickened (about 10 minutes). Set aside; keep warm
Heat remaining oil in skillet over medium heat. Add hot dogs; cook until heated through (about 5-7 minutes), turning occasionally.
Serve hot dogs on buns, top with chili, remaining chopped onion and cheese.