Preheat the oven to 425 degrees F (220 degrees C).
Toss potatoes, garlic, Parmesan cheese, lemon zest, salt, and black pepper together in a bowl. Drizzle with olive oil and toss again until evenly combined.
Heat a cast-iron skillet over medium-high heat. Add butter and heat until melted. Add potatoes; cook and toss until evenly coated with butter, about 2 minutes. Move the skillet to the preheated oven.
Roast in the preheated oven until soft, 15 to 20 minutes, tossing halfway through. Remove from oven and top with parsley.