Preheat the oven to 400 degrees F. Line a sheet pan with parchment paper.
In a small bowl, whisk together the olive oil, melted butter, salt and pepper.
Place a chopstick on either side of 1 potato on a cutting board. Use a paring knife to cut slits about 1/8-inch wide perpendicular to the length of the potatoes. Make sure not to cut the potatoes all the way through. The chopsticks will help stop the knife. Repeat with the remaining potatoes.
Place the potatoes on the sheet pan. Brush with the olive oil-butter mixture.
Roast the potatoes for 45 minutes until the edges are lightly browned and you can easily pierce them with a knife.
Sprinkle the potatoes with Parmesan.
Return the potatoes to the oven and bake for 5 minutes to melt the cheese.
Top the roasted potatoes with chives.
For the herby yogurt, stir together the Greek yogurt, olive oil, chives, garlic, salt and pepper in a small bowl. You can do this while the potatoes roast. Serve the yogurt in a dish or spoon a small amount on the top of each potato.