Begin by trimming away the roots and any tough outer layers. Wash the leeks thoroughly because dirt often hides between the layers. Cut them in half crosswise to make them easier to handle and cook evenly.
Bring a large pot of water to a gentle boil and add the coarse salt, peppercorns, and mustard seeds. Carefully place the leeks into the water and reduce the heat to a simmer. Cook for about 25 to 30 minutes until they become tender when pierced with a fork.
Remove the cooked leeks using tongs and place them on a plate or tray. Allow them to cool completely before handling. Pat them dry with paper towels so the dressing clings properly instead of sliding off.
In a small bowl, whisk together the olive oil, vinegar, and mustard until smooth and slightly creamy. Add the chopped capers, diced shallot, dill, and sugar. Season with salt and black pepper, then whisk again until everything is fully combined.
Taste the dressing before using it. If it feels too acidic, add a tiny pinch of sugar. If it needs more brightness, stir in a little extra vinegar. Balancing these flavors helps create a dressing that complements the delicate leeks perfectly.
Once the leeks are dry, carefully slice them lengthwise so they open slightly. Arrange them neatly on a serving platter or individual plates. Their layered appearance creates a beautiful presentation.
Generously spoon or drizzle the dressing over the leeks. Make sure every section receives some of the flavorful mixture. The dressing slowly seeps into the layers, adding flavor throughout the dish.
Serve immediately at room temperature or refrigerate for several hours. Allowing the leeks to marinate gives the flavors more time to develop and creates an even more delicious final result.