Scrub the potatoes well. Cut them in pieces a little bigger than the tip of your thumb, from the thumbnail up. You want them all to be about the same size so they cook evenly. Place them in a pot and cover with cold water, adding quite a bit of salt, about 1 teaspoon per quart. Bring to a boil and simmer until the potatoes are just tender, 10 minutes or so. Drain.
While the potatoes are cooking, make the dressing. Whisk the mustard, lemon juice and salt in a bowl. Slowly drizzle in the first 2 tablespoons of olive oil. Add the black pepper.
When the potatoes are still warm, but cool enough to handle, peel them to reveal the indigo hue. As they are peeled, put them right away into the dressing, tossing to coat. The potatoes can marinate in the dressing while your prepare everything else.
Clean the leeks and trim them. Slice the white and light green end into thin rounds, less than 1/16-inch thick.
Heat the remaining tablespoon of olive oil in a skillet. Over medium flame, cook and stir the leeks until they are a little crispy and golden on the edges.
Peel the cucumber and cut in half lengthwise. With a spoon, gently scrape out the seeds. Slice 1/8 to ¼-inch thick.
Stir the cooked leeks, cucumbers, hazelnuts, parsley, and blue cheese into the potatoes, mixing well so the blue cheese coats everything. Taste and adjust seasoning, adding more salt and pepper if you think it needs more flavor.
Serve warm or chilled.