Put a skillet over medium heat and drizzle in a 2-count of olive oil. When the oil gets hazy, add the onion and garlic and cook, stirring, until it is 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 more minutes. Stir in the ketchup, chili powder, and mustard and simmer for 15 minutes until thickened. Season with salt and pepper.
While the chili is cooking, get the grill going. 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. Take a few paper towels and fold them several times to make a thick square. Blot a small
amount of oil on the paper towel. Then carefully and quickly wipe the hot grates of the grill to make a nonstick grilling surface.
Bring a pot of water up to a simmer and parboil the dogs for about 5 minutes. Take them out of the water, pat them dry, and grill them just long enough to mark them. (That'll give them a grilled flavor too.) Brush the insides of the rolls with olive oil and lay them face down on the grill; cook until toasty. To serve, put a dog in each roll and top with the chili and some Cheddar.