Leeks look like scallions or green onions with a steriod problem, and although related, are much milder. Select leeks with a clean white slender bulb, at least two to three inches of white, and firm, tightly-rolled dark green tops. The base should be at least 1-/2 inch in diameter, although most are much larger, usually 1-1/2 to 2-1/2 inches. The younger the leek, the more delicate the flavor and texture is. Look for the slim, cylindrical ones rather than those that are large and bulbous. If the bottoms are beginning to round into bulb shapes, the leeks are a bit too mature, and can have a tough, woody center. If the leek is limp at all, pass it up.
2 tablespoons butter
2 tablespoons olive oil
1/2 cup chicken stock
Cut the green and root ends of the leeks off, leaving just the white. You should be left with a piece 4 to 5 inches long. Slice this in half long ways, and then into quarters. Rinse very well, making sure to get water in between -- a lot of dirt gets in there as they're growing.
In a pan, melt butter with the oil over medium heat, then add the clean leeks along with salt and pepper. Cook about 20 minutes until the leeks are soft and begin to slightly brown. Add the chicken stock, and thyme, and raise the heat to high. Cook until stock is reduced and leeks just about begin to caramelize.