In batches, squeeze the liquid from the shredded potatoes with your hands. Put the potatoes in the food processor with the other ingredients and process for 10 seconds. Stop the machine, scrape the bowl with a rubber spatula, and process until the mixture is finely chopped, 10 to 15 seconds more. Transfer the mixture to a large bowl.
Have ready a large plate lined with paper towels. In a 10-inch skillet, heat 1/8 inch of the remaining oil over medium heat until the surface of the oil shimmers very slightly. With a soupspoon, carefully ladle four mounds of the potato mixture into the oil and spread them slightly with the back of the spoon until they are about 3-1/2 inches in diameter. (The oil should be bubbling gently around the pancakes.) Cook until the pancakes are a deep golden color, 2 to 3 minutes. Lift the pancakes with a slotted metal spatula and carefully turn them over. Continue to cook until the second side is a deep golden color, about 2 minutes more. Using the spatula, transfer the pancakes to the paper-towel-lined plate and blot well with more paper towels. Sprinkle lightly with salt. Use the spatula to transfer the pancakes to a baking sheet; keep them warm in the oven while you finish the rest. Continue to add oil between batches as needed to maintain the 1/8-inch level of the oil. Serve with the sour cream and applesauce on the side, if using.