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Leeks have a mild onion-like taste. In its raw state, the vegetable is crunchy and firm. The edible portions of the leek are the white base of the leaves (above the roots and stem base), the light green parts, and to a lesser extent the dark green parts of the leaves.
Trim leeks. Halve lengthwise; rinse well. Add to a pan of boiling salted water. Reduce heat. Simmer until slightly softened, 8 to 10 minutes; drain and pat dry. Brush generously with olive oil. Grill, cut sides down, over medium-high heat, with grill covered, until marked and softened, about 6 minutes. Flip; grill until soft, about 3 minutes. Season with salt and pepper.