Preheat the oven to 425°F (220°C). Line a large baking sheet with parchment paper.
Cut the potatoes in half lengthwise. Pat them dry with paper towels. Rub the cut sides of the potatoes with the olive oil. Season the cut sides with ½ teaspoon salt and ¼ teaspoon black pepper.Place the potatoes cut-side down on the prepared baking sheet and season the skins with the remaining ½ teaspoon salt and ¼ teaspoon black pepper. Bake for 45 minutes, or until the potatoes are fork-tender and the cut sides are lightly golden brown.
Meanwhile, combine the Parmesan cheese, garlic powder, and smoked paprika (if using) in a small bowl.
Remove the baking sheet from the oven. Carefully transfer the potatoes to a plate. Divide the Parmesan mixture into four mounds on the parchment paper, shaping each into an oval slightly larger than a potato half.
Place the potatoes cut-side down on top of the Parmesan mounds, pressing gently so the cheese adheres to the potatoes.
Return the baking sheet to the oven and bake for 10 minutes, or until the Parmesan is melted, deeply golden brown, and crisp around the edges.
While the potatoes finish baking, melt the butter in a small saucepan over medium-low heat. Add the garlic and cook for 30–60 seconds, stirring constantly, until fragrant. Remove from the heat and stir in the chives.
Remove the potatoes from the oven. Let them cool for 2–3 minutes. Using a knife, cut a slit down the center of each potato. Gently press the ends toward the center to open them slightly.
Top each potato with a dollop of sour cream. Spoon the garlic-chive butter over the potatoes and garnish with additional chives. Serve immediately.