Step 1

For the chili: In a large skillet, heat the oil over medium-high heat. Add half the onion and cook, stirring occasionally, until translucent and starting to brown, 3 to 5 minutes. Reserve the remaining onion for serving.

Step 2

Add the beef and garlic to the skillet and cook, breaking up the beef into small pieces with a wooden spoon and stirring occasionally, until the beef is no longer pink, 8 to 10 minutes. Stir in the chili powder, cumin, salt, black pepper, and cayenne and cook until the spices are fragrant, about 1 minute. Add the tomato sauce, ketchup, and mustard, reduce the heat to low, and stir to combine. Let simmer, stirring occasionally, to allow the flavors to meld and the sauce to thicken slightly, about 15 minutes. Keep the chili warm on the stove over low heat while you prepare the hot dogs.

Step 3

For serving: To assemble the chili dogs, heat through the hot dogs using your preferred method (in simmering water, seared in a pan with 1 to 2 tablespoons butter, or on a grill). Place the hot dogs in the buns and top with a generous scoop of chili. Garnish with some cheddar and as much or as little of the reserved onion as you like.