Put ground beef, diced onion, and minced garlic in a food processor fitted with the chopping blade. Pulse the meat mixture several times until the meat is smooth. When the meat cooks, it will break apart into very small crumbles which is exactly what you want to happen.
In a large skillet over medium heat, cook the beef-onion-garlic mixture for two or three minutes. Stir frequently to keep meat broken up.
Add the chili powder, salt, garlic powder, onion powder, and black pepper and continue to cook for several more minutes until the beef and onions are cooked through. Stir frequently.
Add the tomato paste, water, brown sugar, Worcestershire sauce, and apple cider vinegar. Stir well and bring to a simmer. Set a lid slightly ajar on the skillet and continue to simmer over low heat for 30-45 minutes, stirring as needed. When the chili has thickened to your preference remove from heat.
To assemble chili dogs: place hot dogs in the buns. Squirt some mustard down one side of the hot dog. Spoon chili over hot dog and mustard. Sprinkle with grated cheddar cheese and finely chopped onions.