Preheat the oven to 425°F and line a baking sheet with parchment paper.

Place one of the potatoes on a cutting board and lay butter knives or chopsticks along both of its long sides. Use a sharp knife to cut the potato crosswise into ⅛-inch-thick slices, stopping when your knife reaches the butter knives or chopsticks so that the potato stays intact at the bottom. Repeat with the remaining potatoes.

Place the potatoes on the baking sheet. Drizzle with olive oil, sprinkle with salt and pepper, and use your hands to coat, ensuring oil and seasonings reach between the potato slices. Slide a sage leaf into each of the cracks between the potato slices. Drizzle with a little more olive oil and roast for 50 minutes.

Remove the potatoes from the oven and brush with the garlic butter. Roast for another 25 minutes, or until the potatoes are tender in the middle and crisp around the edges. Season to taste with salt and pepper and top with parsley and red pepper flakes. Serve with more garlic butter on the side.