
Preheat the oven to 425˚F. Using a small, sharp knife, score the potatoes. Place the butter in a 9x13-inch baking dish and set it in the oven for 5 minutes, until the butter melts.
Remove the baking dish from the oven and reserve 1 tbsp of melted butter. Add the Parmesan cheese and spices to the remaining butter in the baking dish. Stir until well combined, and they form a paste. Spread with a spatula to coat the bottom of the pan.
Place the halved potatoes cut-side down in the baking dish. Brush with the reserved melted butter on top. Bake until golden brown and crispy, about 35 minutes.
Separate the potatoes and serve with ranch dip, if desired.