Prepare a large bowl of cold, generously salted water. Peel the potatoes and transfer peeled potatoes to the salted water. Julienne the potatoes using a mandoline (this is my preferred method) or shred them with a box grater or food processor cheese grater attachment. Transfer the julienned/shredded potatoes back into the salted water and allow to sit for 10-15 minutes. While the potatoes soak, shred the onion and set aside.
Drain the potatoes. Divide the drained potatoes between two clean flour sack towels or two large pieces of doubled over cheesecloth. Divide the shredded onion in half, placing one half on top of each pile of potatoes. Working with one pile at a time, pull the ends of the towel or cheesecloth together and wring out as much moisture as possible from the potatoes and onions. (This is the hard part. I recommend wrangling in a friend, or relative to help.) Repeat with the second pile of potatoes and onions.
In a large bowl, (you can use the salt water bowl, just rinsed and dried) beat the eggs for 1 minute until well combined and slightly lighter in color. Add the potatoes and onions to the bowl, followed by the matzo meal, potato starch, and salt. Mix together with your hands until well combined, about 2-3 minutes. As you mix, the matzo meal and potato starch will become moistened, making the mixer thicker and sticker. The extra time spent mixing and massaging with your hands will make for a mixture that sticks together excellently!
Heat 1/2” of oil in a cast iron or heavy bottomed pan to 325F, and prepare a rimmed baking sheet with a wire rack for cooling. While the oil heats, use a ¼ cup measuring cup to scoop the latke mixture. Place the scoops on a clean surface and use a spatula to squish to ½” thick. (If the latkes are too thick, they may not cook evenly throughout.) I like to prepare about 5-6 scoops at a time.
When the oil is hot, lower 2-3 prepared latkes into the pan using a heat-proof slotted spatula. Fry the latkes 2 minutes per side, or until golden brown. As always with frying, check your oil temperature often and adjust the heat as needed. Transfer the latkes to the prepared wire rack to cool and sprinkle with salt.
If you like, keep the latkes warm in a 200F oven, or make them ahead and reheat on a wire rack when ready to eat. Serve with creme fraiche or sour cream, applesauce or apple butter, and a sprinkle of thinly sliced chives.