Heat the oven to 350°F and arrange a rack in the lower third. Place the butter, thyme, garlic, salt, and pepper in a small saucepan over low heat, stirring occasionally, until the butter has melted and the salt has dissolved, about 8 minutes. Turn off the heat. Place 1 potato on a cutting board and make parallel crosswise cuts about 1/8 to 1/4 inch apart, leaving at least 1/2 inch of the potato’s base intact. Repeat with the remaining potatoes. Place the potatoes cut-side up in a 13-by-9-inch baking dish. Remove and discard the thyme sprigs and garlic from the butter mixture. Evenly drizzle about half of the butter mixture over the tops of the potatoes. Cover the dish tightly with aluminum foil and bake for 40 minutes. Remove from the oven, uncover, and evenly drizzle the remaining half of the butter mixture over the potatoes (rewarm over low heat if the butter has solidified). Cover with the foil and bake for another 20 minutes. Remove from the oven, uncover, and baste with the browned butter in the bottom of the dish. Cover with the foil and continue to bake until the potatoes are fork-tender, about 20 minutes more. Transfer to a serving dish and drizzle with the remaining butter in the dish. Sprinkle with the chives and serve.