Peel potatoes and onions, and finely grate using a box grater. Place in a strainer set over a bowl and let drain, squeezing mixture until dry; transfer to another bowl. Slowly pour off the water from squeezing the potatoes until you reach the milky starch at the bottom of the bowl; pour this on top of the drained potato mixture. Add flour and eggs, and season with salt and white pepper; mix until evenly combined.
Heat 1⁄4 cup oil in an 8" skillet over medium heat. Working in batches, measure out 1⁄2 cup potato mixture, and use your hands to flatten it into a 4-5" pancake; add to skillet, and fry, flipping once, until golden brown and cooked through, about 8 minutes. Transfer to a paper towel-lined baking sheet, and repeat with more oil, as needed, and remaining potato mixture. Serve pancakes with applesauce on the side.