Preheat oven to 400 degrees. Place garlic on parchment-lined foil. Season with salt and pepper, generously drizzle with oil, and wrap. Roast until fragrant and soft, about 1 hour. Leave oven on.
Cover potatoes with salted water by 2 inches in a medium saucepan. Bring to a boil, and cook until fork tender, about 20 minutes. Drain, and return to hot pan. Let stand for 5 minutes to dry.
Halve potatoes crosswise. Trim (and reserve) rounded ends of each half slightly, so potatoes sit flat with cut sides up. Scoop out flesh using a melon baller, leaving a thin layer on bottom and sides, and transfer to a bowl. Peel reserved ends; add to bowl. Stir in oil, sour cream, and thyme. Squeeze garlic cloves from skins into potato mixture. Mash until smooth. Season with salt and pepper.
Lightly brush a baking sheet with oil. Fill each potato half with about 1 teaspoons potato mixture, mounding slightly. Place potatoes 1 inch apart on sheet, and lightly drizzle with oil. Bake until golden brown, 25 to 30 minutes.
Bring to room temperature, and bake just before serving.