Place a large skillet in the oven and preheat to 325°F.
Cut the white part away from the green part of the leek, and reserve the green part of the leek for another recipe.
Slice the root of the leek (the white part) about 1/8 of an inch from the bottom of the leek, and discard the root.
Cut the remaining white part of the leek into 2-3 inch pieces (depending on the size of the leek).
Place the butter and olive oil in the skillet and place the leeks,standing up on end in the pan.
Return the skillet to the oven and roast for about 15 minutes.
Turn the leeks over to the other cut side and roast for an additional 10 minutes.
Add the salt and vegetable stock and return the pan to the oven.
Braise the leeks for another 25 to 30 minutes until most of the liquid has evaporated.
Serve.
