Prep the veg - Trim and peel the asparagus, if necessary, and cut into 2 or 3-inch lengths. Destem the sugar snap peas. Blanch the asparagus and the peas into boiling water and cook until just crisp-tender, then scoop them out of the water and plunge them in an ice water bath. Set aside, reserving a few asparagus tips for garnish, and leave the pot with the hot water on the stove (you'll use the same pot to cook the potatoes). Mince the shallots and slice the radishes very thinly. Chop the mint and the dill.
Cook the potatoes - Prick the potatoes and add them to the pot of hot water. Bring to a boil, then reduce to a simmer, and cook until the potatoes are the consistency you like for potato salad. Drain the potatoes and add them to a large bowl with the minced shallots. Toss the potatoes and shallots with a generous glug of Preserved Lemon Vinaigrette.
Assemble the salad - After the potatoes have cooled a bit (but not completely), add the peas, asparagus, and mint, and gently toss to combine. You don't want the potatoes to so warm that they further cook the peas and asparagus, but you do want them to be warm enough to slightly wilt the mint leaves. Then scatter the radish slices and dill on top, and garnish with asparagus tips.