Pre-heat the oven to 425˚F.
In a large pot, cover the fingerling potatoes with cold, salted water and bring up to a boil. Cook until just tender, about 8 minutes, then drain.
While the potatoes cook, melt the butter in a small pot with the garlic and cook over medium-low heat for about 4-5 minutes. Pour the melted butter onto a baking sheet, then place the potatoes on top, cut-side down. Roast until deeply golden brown, about 20 minutes.
Remove the potatoes from the oven and flip them over with a spatula. Season with some salt and sprinkle with the Parmigiano Reggiano cheese and lots of black pepper. Return the potatoes to the oven for 5 more minutes until the cheese is melted.