Place the potatoes in a large pot and fill with water until potatoes are just covered. Place on the stove and bring to a boil.
Boil the potatoes for 5 minutes.
Remove from heat, drain, and allow potatoes to cool to room temperature or until cool enough to handle.
Heat your oven to 400°F
Cut potatoes in half, then in half again, or in quarters until you have one-inch pieces. Place potato pieces in a bowl.
In a separate bowl, combine oil, melted butter, garlic, Parmesan, salt, & pepper. Pour over potatoes and toss to coat.
Arrange potatoes in a single layer on a parchment or foil lined baking sheet.
Roast in the oven for 30 minutes, turning halfway through.
Remove roasted potatoes from the oven and arrange on a platter.
Drizzle the gremolata over the potatoes. Spoon the Greek yogurt onto the center of the potatoes, or serve in a separate dish on the side.