Wash and scrub the potatoes but leave the peels on. Cut baby/new/fingerling potatoes in half; cut larger potatoes into chunks.
Transfer the potatoes to a saucepan and cover with an inch of cold water. Season generously with kosher salt. Bring to a simmer and maintain a decent simmer for 8 to 12 minutes until just tender. If the fork pierces the potatoes with the slightest bit of resistance, the potatoes are done. Note: For reference, the halved baby red potatoes I used took only 8 minutes. Meanwhile, make the dressing. In a large bowl, whisk together the tahini, yogurt, Dijon mustard, yellow mustard, garlic, lemon zest, lemon juice, celery seeds, caper brine (not the whole capers), 1 teaspoon kosher salt, and pepper until well combined. Add 1 tablespoon of the chopped dill and stir together.Note: If the dressing is too thick, whisk in a tablespoon of cold water.
Once the potatoes are cooked, drain them in a colander (reserve a little of the cooking liquid in case it's needed). Let the potatoes rest in the colander for 5 minutes to dry out, but don’t wait until they have cooled down.
Add the warm potatoes to the dressing and coat evenly and well. If needed, add a spoon of the cooking water to bring everything together (I didn't need to).
Add the capers, red onions, and jalapeños to the potato salad, and toss again gently. Sprinkle the remaining dill and the chives on top before serving. Season to taste with salt and pepper.
Serve warm, or chill for at least 1 hour.