Preheat your oven to 425°F (220°C).
Place a potato between two chopsticks or wooden spoons. Make thin slices across the potato, about 1/8 inch apart, without cutting all the way through. The chopsticks or spoons will act as a guide to prevent you from slicing the potato fully.
Repeat the slicing process with all the potatoes.
In a small bowl, mix together the melted butter, olive oil, minced garlic, salt, and black pepper.
Brush the butter mixture generously over the potatoes, making sure to get in between the slices.
Place the potatoes on a baking sheet lined with parchment paper or foil.
Bake for 30 minutes, or until the potatoes are tender and crispy on the outside.
Remove the potatoes from the oven and sprinkle them with grated Parmesan cheese, making sure to get some in between the slices.
Return the potatoes to the oven and bake for another 5 minutes, or until the cheese is melted and slightly golden.
Remove from the oven and garnish with fresh chopped parsley.
Serve the mini hasselback potatoes hot as a delicious side dish or appetizer.