Preheat the oven to 425 degrees F.
Peel potatoes. Cut each potato not quite through in a series of crosswise slices about 1/4-inch apart or closer so that they are still joined together at the bottom. Brush the potatoes with the melted butter and place in a small baking pan. Pour the chicken stock around the potatoes and sprinkle with the thyme leaves. Sprinkle with salt and pepper and roast until the potatoes are half cooked, 25 to 30 minutes, basting every 5 minutes with the butter-chicken stock mixture.
In a small bowl combine the grated cheese and bread crumbs and divide the mixture evenly between the tops of the 2 potatoes. Continue roasting without any further basting until the potatoes are crispy on the outside and cooked through, about 30 minutes.
*Note: Exact cooking time will depend on the size of the potatoes.