1. Heat oven to 450 degrees F.
2. Combine butter, oil and garlic in a microwave proof cup. Cover with plastic wrap and microwave on Medium-High 1 minute, until butter melts. Let stand, covered, 5 minutes; remove garlic.
3. Arrange one potato flat side down on a work surface. With a small, sharp knife, make four crosswise cuts into the top of potato, two thirds of the way through, being careful not to cut all the way through. Cut 3 sprigs of thyme into 1/2-inch pieces. Using the tip of the knife, divide and tuck pieces into each slit. Repeat process with remaining potatoes and thyme.
4. Transfer potatoes to a jelly-roll pan. Drizzle cut sides of potatoes with melted-butter mixture, and sprinkle with salt and pepper. Bake 50 to 55 minutes, until tender when pierced with a knife. Makes 4 servings.