Preheat a well-oiled grill to medium-high heat. Place hot dogs on preheated grill and cook with grill lid covered, until nicely marked on all sides and heated through, 4 to 5 minutes, or until desired degree of doneness. Remove hot dogs from the grill and keep warm until ready to serve.

Brush the cut sides of the hot dog buns lightly with the olive oil. Place cut side down on the grill and cook, with the grill lid open, until lightly toasted. Serve buns immediately with grilled hot dogs, Jalapeno-Cheese Sauce, and assorted garnishes.