Peel the potatoes and then grate them using a hand grater (use a medium shred) into a bowl of ice water. Set aside and let rest for about 10-15 minutes.
While the grated potatoes are resting, peel and grate the onion into a large bowl.
Remove the shredded potatoes from water and place into a cheesecloth. Gently squeeze the potato water back into the bowl. Let the potato water sit for about 10 minutes to let the starch sink to the bottom. After 10 minutes, carefully drain the potato water from the bowl, reserving the starch at the bottom. Scrape the starch with a spatula and set aside.
Combine the squeezed potato shreds with the onion into a mixing bowl. Season liberally with kosher salt and freshly ground black pepper. Mix everything by hand and then let sit for about 10 minutes, as the potato and onions will start to "sweat" from the salting.
Place the potato and onion mixture back into the cheesecloth and squeeze out excess moisture into the sink, and place the mixture back into the empty mixing bowl.
Spoon in the reserved potato starch and crack two large eggs into the bowl. Gently massage the starch and eggs into the potato mixture by hand until well combined.
Pour up to an inch of vegetable oil into a large skillet and heat over medium-high flame up to 360-375 degrees F.
Scoop out a golf ball-sized amount of the potato mixture and press it firmly between your hands to form a 3-inch round, 1/2 inch thick pancake and set aside on parchment paper until ready for frying
Once the oil has reached frying temperature, gently place up to 4 latkes in the skillet at one time. Fry on each side about 3-4 minutes until golden brown.
Place finished latkes on wire rack and cool for about 5 minutes before serving. (You can place the wire rack on a cookie sheet in a warm oven to keep them warm until all the latkes are fried.)
Serve warm with a generous dollop of applesauce and sour cream