Using starchy potatoes is essential for making German potato pancakes. Russet, Idaho and Yukon Gold potatoes all work. There is no flour in these potato pancakes so they're gluten-free. The natural starch from the potatoes binds the mixture together. The potato pancakes should be served straight from the pan or oven (you can skip the oven part if you don't mind standing at the stove while everyone else is eating).
Scrub potatoes well and remove any eyes and blemishes. Cut the potatoes into wedges that will fit through the food chute of a food processor. Attach the shredding disk to the food processor. Pass the potato wedges through the food chute to shred. You should have about 5 loosely packed cups. Remove the shredding disk and insert the blade. Pulse the potatoes until very finely chopped but not quite a smooth puree, 4 to 5 times.
Line a fine-mesh strainer with a clean dish towel and place over a large bowl. Scrape the potatoes into the colander and set aside to drain.
Meanwhile, pulse onion in the food processor until finely chopped.
Press down on the potatoes a couple of times to exude remaining liquid, then pick up the corners of the towel and twist to squeeze out as much liquid as possible over the colander and into the bowl. Let the potato liquid stand for a few minutes until the white potato starch settles at the bottom. Carefully pour off the liquid, retaining the starch in the bowl. Add the potatoes to the starch, using a silicone spatula to scrape them off the towel. Add the onion, eggs, salt and pepper. Stir well to combine.
Preheat oven to 350°F. Coat a large baking sheet with cooking spray.
Heat 2 tablespoons oil in a large nonstick skillet over medium-high heat until hot enough to sizzle a shred of grated potato. Mound 4 pancakes in the hot oil, using a heaping ¼ cup potato mixture each. Gently flatten the mounds to make 3-inch pancakes. Cook, flipping once halfway, until golden brown, 2 to 3 minutes per side. (Reduce heat, if necessary, to prevent burning.) Transfer to the prepared baking sheet.
Repeat to make 2 more batches of pancakes, using an additional 1 tablespoon oil to make each batch. Stir the potato mixture well before scooping out more pancakes.
Bake the potato pancakes until sizzling, about 10 minutes. Serve with applesauce, if desired.