Add 1 cup water to the drip tray on Kenyon Grill; preheat grill to high heat. Cut off a thin slice of each potato lengthwise to create an even base for the potatoes to rest on.
Rinse potato under running water, fanning out to rinse inside of cut slits. Place potatoes on a plate and microwave at high for 5 minutes. Flip potatoes over and microwave again for an additional 5 minutes.
Tuck slices of garlic and Parmesan in slits in the potatoes. Brush potatoes with olive oil and season with salt and pepper to taste. Sprinkle tops with grated Parmesan.
Place potatoes on grill, cover, and cook until soft in the center and crisp around the edges, about 30-40 minutes. Remove from the grill, let cool for 5 minutes, then serve immediately while still warm.