In a large skillet over medium-high heat, add vegetable oil. Once the oil is hot, add hot dogs and cook until they are browned on all sides. Remove and set them aside.
Sauté the Onions and Garlic: In the same skillet as the hot dogs, add the chopped onions and minced garlic. Sauté for about 3 - 4 minutes until the onions become translucent.
Push the sautéd onions and garlic to the side of the skillet and add ground beef to the center. Cook the ground beef until it's browned, breaking it into small pieces with a spatula as it cooks. Stir in chili powder, ground cumin, paprika, and cayenne pepper into the ground beef mixture.
Add ketchup and yellow mustard, mixing well to combine. Season with salt and black pepper to taste.
Reduce the heat to low and let the sauce simmer for about 5 minutes, allowing the flavors to meld.
Assemble the Coney Dogs: Place each hot dog into a bun, spoon a generous amount of chili sauce over each hot dog, top each Coney dog with chopped onion, Serve coney dogs with carrots and ranch and apple juice.