To make the chili: Heat a skillet over medium flame and add 2 tablespoons of olive oil. When the oil gets hazy, add the onion and cook, stirring, until they are soft and translucent, about 5 minutes. Add the ground beef, breaking it up with the back of a spoon, and cook until nicely browned, about 10 minutes. Stir in the ketchup, chili powder, and mustard; simmer for 15 minutes until thick; season with salt and pepper.
For the hot dogs: While the chili is cooking: place a large grill pan on 2 burners over medium-high heat or preheat an outdoor gas or charcoal barbecue and get it very hot. Brush the grates with oil to keep the hot dogs from sticking. Parboil the dogs first before grilling: bring a pot of water to a boil and cook the hot dogs for about 5 minutes. Remove from the water and grill the hot dogs just long enough to give them grill marks. Brush the insides of the rolls with the remaining oil and place them face down on the grill until toasty. To serve, top each hot dog with the chili and some Cheddar cheese.