Add the onion and cook until sweating, about 3-4 minutes.
Add the ground beef and cook over medium-high heat until well-browned, about 8-10 minutes.
Add tomato paste, ketchup, Worcestershire sauce, vinegar, salt, pepper, paprika, cumin, ginger, and cayenne, and stir together, making sure all the meat is broken up into small pieces.
Add the chicken stock and bring to a simmer.
Stirring occasionally, simmer over low heat until chili thickens, about 10-12 minutes.
Serve over hot dogs and garnish with shredded cheese.