Look for: Long, thin stalks that do not bend and are not bruised; the outer layers should not be wrinkly or dried out.
Prep: Trim off the thick green leaves, leaving only the pale green and white parts; pull off damaged outer layers, leaving the root end intact. Split in half lengthwise. Under cold running water, fan out inner layers to rinse out grit and sand.
Braise: Place leeks in a large skillet with 1/2 cup vegetable (or chicken broth), 1 sprig fresh rosemary (or 6 juniper berries and 6 black peppercorns). Bring to a simmer over high heat. Cover, reduce heat and cook until tender, about 12 minutes. Serve warm or cold with a vinaigrette dressing.
Grill: Preheat grill. Brush leeks with 1 tablespoon extra-virgin olive oil. Place over direct, medium heat and grill, turning occasionally, until lightly browned, about 8 minutes.
Roast: Preheat oven to 500°F. Trim off root ends of leeks, slice in half crosswise and then into 1/4-inch-thick slices lengthwise. Spread on a baking sheet or pan large enough to hold them in a single layer. Coat with 2 teaspoons extra-virgin olive oil. Roast, stirring once halfway through cooking, until browned and tender, 10 to 15 minutes.
Sauté: Thinly slice leeks into half-moons. Heat 1 tablespoon butter in a large skillet over medium heat. Add leeks; cook, stirring often, until softened and very aromatic, about 5 minutes.