Heat a large skillet over medium heat and add 1 tablespoon olive oil. Add 1 chopped onion and 2 chopped garlic cloves and cook, stirring, until soft and translucent, about 5 minutes. Add 1 pound ground beef, breaking it up with the back of a spoon, and cook until nicely browned, about 10 minutes.
Stir in 2 1/2 cups ketchup, 1 teaspoon chili powder and 2 tablespoons yellow mustard and simmer until thickened, about 15 minutes. Season with salt and pepper.
Grill 4 hot dogs over medium-high heat, turning, until marked. Serve on grilled buns and top with the chili and shredded cheddar.