We prefer to use leeks measuring 1 inch or less in diameter for this recipe because they’re more tender than larger leeks. Larger leeks will work, but discard their first two outer layers because they tend to be fibrous. Orienting the leeks in one direction makes them easier to transfer in and out of the skillet. When trimming the leeks, be careful to leave the root ends intact so that the layers stay together when the leeks are halved. If you don’t have a small jar with a lid, whisk the vinaigrette together in a bowl.

Trim roots from leeks, leaving ends intact so layers stay together when halved. Halve leeks lengthwise, wash thoroughly between layers to remove any dirt, and pat dry with paper towels. Season cut sides with salt and pepper.

Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add half of leeks to skillet, with root ends pointed in same direction, and cook until browned, about 2 minutes per side. Transfer to plate. Repeat with 1 tablespoon oil and remaining leeks.

Return all leeks to skillet, facing same direction. Add broth and bring to boil. Cover, reduce heat to medium-low, and simmer until leeks are tender when poked with tip of paring knife, 10 to 12 minutes. Using slotted spatula, transfer leeks to shallow serving platter, leaving braising liquid in skillet.

Increase heat to medium-high and bring braising liquid to boil; cook until reduced to about 2 tablespoons, 2 to 4 minutes. Transfer braising liquid to small jar and add vinegar, mustard, garlic, remaining ¼ cup oil, ¼ teaspoon salt, and ¼ teaspoon pepper. Affix lid and shake jar vigorously until vinaigrette is emulsified, about 15 seconds. Spoon vinaigrette over leeks. Sprinkle with tarragon and serve.

Prepping Leeks for Braising