Prepare the hard boiled eggs if needed (see notes for an easy how-to). Peel and dice small.
Place the potatoes in a large pot with enough water to cover the potatoes by 1 inch. Salt the water generously. Bring the water to a boil over medium-high heat. Cook until potatoes are just tender when pierced with a fork, 10 to 20 minutes depending upon their size. DO NOT overcook, or your potato salad may be mushy.
Prepare the dressing: To a food processor or blender, add the Greek yogurt, olive oil, vinegar, mustard, garlic, celery salt, and black pepper. Cut 2 of the green onions into 4 pieces each and add them to the food processor as well.
Finely chop the third green onion and set aside. Blend the dressing until smooth, stopping to scrape down the sides of the food processor a few times as needed.
Drain the potatoes. As soon as you can handle them safely, cut potatoes into 1 1/2-inch chunks (depending upon the size of your potatoes, this will be either halves or quarters). Transfer to a large bowl.
While the potatoes are still hot, pour 3/4 of the dressing over the top.
Gently stir to combine (it will look like a lot of dressing). Let sit 10 minutes, stirring once or twice as it rests.
Add the celery, capers, and eggs. Reserve a tablespoon or so of the remaining chopped green onion for garnish, then add the rest to the bowl. Stir to combine. Taste and add more salt/pepper as needed. Refrigerate until ready to serve.
Just before serving, add the remaining dressing as desired, taste once more for salt (potatoes drink it up! I usually add a few big pinches), and sprinkle with the reserved green onion. Enjoy!
Notes
*To Hard Boil Eggs. Place the eggs in a small pot with enough water to cover. Bring to a boil over high heat. As soon as the water boils, immediately remove the pot from heat and cover for 8 minutes. Prepare an ice bath. After 8 minutes, transfer the eggs to the ice bath to cool.
To STORE. Store leftover potato salad in the refrigerator for up to 3 days. Taste and season with additional salt before serving.
To FREEZE. No you cannot freeze potato salad (sorry!). The potatoes will become mushy and the dressing will separate.