Cut off the dark green leaves from the top of each leek. Trim the root while leaving enough to hold the leek together. Slice the leek in half lengthwise and rinse in between the layers. Tie the leeks back together so they won't fall apart while poaching.
Fill a deep skillet, or wide pot, with water and bring to a boil. Season the water generously with kosher salt, it should taste lightly salted. When the water boils, add the leeks and turn the heat down to maintain a gentle boil. Cook the leeks for 12-15 minutes until they are tender.
While the leeks are cooking, prepare an ice water bath. Transfer the cooked leeks to the ice water to cool them down. Once, cool transfer the leeks onto paper towels and pat dry. Cut off the strings and carefully separate the halves. If part of the root is still attached, trim it off.
In a small bowl, combine the Dijon mustard, grainy mustard, ½ tsp kosher salt, pinch of pepper and sherry wine vinegar. Whisk together. Slowly add the light olive oil, whisking constantly. Keep whisking until the dressing comes together and is fully emulsified. Add the shallots and chopped dill and stir to combine.
To serve, arrange the leeks on a serving platter. Spoon the vinaigrette over, making sure to cover the leeks evenly. The leeks can be made and dressed a few hours before serving and kept in the fridge. Garnish with more chopped fresh dill and enjoy!