Use a peeler or paring knife to peel the tough fibrous layer of skin off of the broccolini. If you're using a paring knife, look at the cut end of the stem, and you can see a ring of light-colored fibers, insert the blade of the knife just under that layer and then peel away the tough outer layers. Then you can turn the stem and repeat.
Cut the broccolini into manageable pieces.
Bring a large pot of well-salted water to a rolling boil and boil the broccolini until it's cooked to your liking. I usually let the water return to a boil and cook it for another 1 minute.
Mix the mayonnaise, Dijon mustard, pickled mustard seeds, and salt together in a small bowl.
When the broccoli is cooked, drain it and shake off any excess water. Add it to a bowl with the dressing and stir to coat.
Plate the broccolini with the smoked salmon.
Top the salad with some soft-boiled eggs and a crack of freshly ground black pepper.