Preheat oven to 425 degrees F.
Give your potatoes a very good scrubbing since we’re leaving the skins on. Grate the garlic cloves and set aside.
Slice a thin layer off the bottom of each potato. This will serve to give them a solid base to rest on while they get sliced. Using a sharp knife, make slices across the potato, about 1/8 of an inch apart, slicing into them, but not completely through them. The slices should stay connected at the bottom. Repeat with each potato.
Starting at one end, begin to slide garlic slices and thyme in between potato slices until you reach the end of the potato. I found this to be the easiest method in preventing breakage. If you start sliding garlic -n- thyme in the middle you may end up having to shove in the garlic and risk breaking your nicely sliced potato.
Place potatoes on a baking sheet. Generously sprinkle potatoes with salt and drizzle with oil. Pour the melted butter over the potatoes and sprinkle with as much grated parmesan cheese as you dare.
Bake for 1 hour or until tender on the inside and crisp on the outside. Remove the pan about every 15 minutes to baste potatoes in the oil and butter from the pan.