In a medium skillet, cook the ground beef over medium heat until browned. Drain any excess fat.
Add the chopped onion, chili powder, salt, allspice, dry mustard, black pepper, cumin, and cinnamon to the skillet with the beef. Stir well to combine.
Mix in the tomato paste and water. Bring the mixture to a boil.
Reduce the heat to low and let the sauce simmer for 1 to 2 hours, stirring occasionally, until thickened and the flavors have melded together.
Spoon about 2 tablespoons of the sauce over each hot dog.
For an extra touch, garnish with additional chopped onion, mustard, or shredded Cheddar cheese as desired.