In a medium pot, add the potatoes and fill with enough water to cover by 1-2 inches. Add 1 tablespoon of salt (this will help season the potatoes, you’ll be throwing most of it away with the water).
Bring to a boil, then reduce the heat to medium-low and simmer rapidly for 15-20 minutes, or until easily pierced with a knife (this will vary greatly depending on the size of your potato). Drain the potatoes and transfer to a cutting board to cool off for a few minutes, then cut them into bite-sized pieces.
While the potatoes are still warm, transfer them to a large bowl and sprinkle with salt (about ½ teaspoon) and a splash of vinegar and toss to coat (doing this while they’re warm will ensure that the potatoes are nicely seasoned).
To the large bowl, add the cucumber, radish, snap peas, parsley (if using), scallions, and avocado.
(Make the Tahini Dill Sauce if you haven’t already, instructions below).
Mix the lemon into ¾ cup of Tahini Dill Sauce. You should have a drizzle-able dressing. If it’s too thick, add more lemon (the dressing will be thick if it’s been refrigerated but it will loosen up as it sits at room temp).
Pour just under half of the dressing all over the veggies and gently toss to coat. Serve topped with more dressing, a sprinkle of salt and pepper, a generous drizzle of good olive oil, and any toppings of choice (highly recommend at least topping with feta).