Using a wooden spoon as a cradle, place each potato in the spoon and make several vertical slits, being careful not to cut all the way through. You can also place chopsticks on either side of the potato to keep your knife from slicing through.
Arrange the potatoes on a baking sheet.
Combine the melted butter, oil, and garlic, then brush each potato with this mixture.
Sprinkle with salt, pepper, and bake for 20 minutes.
Take the potatoes out of the oven, brush them again, and sprinkle with most of the parmesan.
Return to the oven for about another 20 minutes or until the potatoes are golden and the flesh is soft.
Remove the garlic parmesan mini hasselback potatoes from the oven, sprinkle with the remaining parmesan and chopped parsley, and serve immediately.