Trim off leek tops where they turn dark green, and the bottoms just above the roots. Split the leeks almost in half horizontally. Rinse the leeks extremely well in cold running water; dirt may hide in between the leaves, so check carefully.
Reshape the leeks and tie with kitchen twine at each end. Or, you don’t have to. You can simply simmer them gently without stirring, but you do risk the chance of them separating.
Set aside a baking sheet lined with a clean kitchen towel. Place the cleaned leeks in a single layer in a 2-quart saucepan and cover with water. Season with salt and pepper. Add the fresh bay leaves. Bring the liquid to a boil, reduce the heat to a simmer and cook until tender, about 30 minutes.
Meanwhile, prepare the Dijon vinaigrette: Combine the mustard, garlic, shallot, and white wine vinegar. Whisk in the oil until smooth. Taste and adjust for seasoning with salt and pepper. Set aside.
Remove the leeks from the cooking liquid. (Reserve the liquid for another use.) Using a slotted spoon, transfer them to the prepared baking sheet lined with a kitchen towel to drain. Pat dry.
Place the leeks in a shallow dish and pour the Dijon vinaigrette on top. Turn to coat. Refrigerate until chilled, about 30 minutes. Taste and adjust for seasoning with salt and pepper. Top with dill and serve immediately.