Bring a large pot of water to a boil. With kitchen twine, tie the leeks into 2 bundles, with the green tops at the same ends. Add the bundles to the boiling water. Reduce heat, and simmer until the leeks are tender, about 15 minutes. Remove the leeks; rinse under cold water. Drain well, and gently pat dry with paper towels. Set aside.
Make the vinaigrette: In a large bowl, whisk together the mustard, vinegar, garlic, and basil. Slowly whisk in the oil in a fine stream. Whisk in the salt and pepper.
Gently toss the leeks in the bowl with the vinaigrette, coating well. Serve chilled or at room temperature.
