Step 1

Preheat oven to 350°. Toast walnuts on a rimmed baking sheet, tossing once, until golden brown, 6–8 minutes. Let cool, then coarsely chop. Transfer to a small bowl and toss with oil; season with salt.

Step 2

Trim root ends of leeks and 1" from the dark green tops. Cut leeks into ½"-thick rounds (the dark green parts won’t be rounds, but that’s okay). Rinse well.

Step 3

Cook leeks in a large pot of boiling salted water until meltingly tender, 12–15 minutes. Transfer to a bowl of ice water to stop the cooking. Drain and pat dry.

Step 4

Whisk garlic, vinegar, and Dijon and whole grain mustards in a small bowl; season vinaigrette with salt.

Step 5

Arrange leeks on a platter; drizzle with vinaigrette and let sit at least 10 minutes (the longer, the better).

Step 6

Just before serving, scatter walnut mixture over leeks and top with tarragon and lots of pepper.

Step 7

Do Ahead: Leeks (without walnut mixture and tarragon) can be marinated 1 day ahead. Cover and chill. Bring to room temperature before serving.