Place a potato on the cutting board and place a chopstick or the handle of a wooden spoon on each side of the potato. This will prevent you from slicing through the potato. Make thin crosswise slices the entire length of the potato, leaving at least 1/4-inch of the bottom unsliced. Repeat with the remaining 3 potatoes. Place the potatoes on the prepared baking sheet.
Heat the oil and garlic in a small saucepan over medium heat. When the oil is hot and aromatic, remove and discard the garlic slices. Brush the oil over the potatoes, letting some of the oil drizzle into the cuts.
Sprinkle the potatoes lightly with kosher salt and black pepper.
Bake the potatoes for about 1 hour, or until they are fork-tender and the skin is crisp.
Sprinkle the Hasselback potatoes with chopped chives or parsley just before serving.