Fill a large saucepan with water and bring to a boil. Add the leeks and simmer for 3 minutes. Add the asparagus and continue simmering about 3 minutes more, until both the asparagus and leeks are tender but green. Transfer both to a bowl of ice water to cool, then drain them, dry them, and arrange them on a serving platter.
Combine the mustard, vinegar, and olive oil in a bowl. Spoon the vinaigrette over the leeks and asparagus. Top with the halved eggs and scatter with chopped capers and chives. Season generously with salt and pepper.
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