Peel the potatoes and place them immediately in a bowl of cold water to prevent discoloration. Chop three of the potatoes and the onion into 1-inch chunks, reserving the last potato in the water until needed.

Transfer the chopped potatoes and onion to a food processor. Pulse several times until the mixture forms a coarse puree. Scrape down the sides of the bowl as needed to ensure even texture.

Line a colander with a large square of folded cheesecloth (about four layers thick). Pour the potato-onion mixture into the cheesecloth and gather the corners together. Twist and squeeze firmly to remove as much liquid as possible—up to one cup of moisture may be released. Set the squeezed mixture aside in the cheesecloth to limit oxidation.

Using the coarse side of a box grater, grate the remaining potato and add it to the drained potato-onion mixture.

In a large mixing bowl, transfer the potato mixture and stir in the flour, eggs, salt, and black pepper. Mix thoroughly until all ingredients are evenly combined and the mixture has a cohesive consistency.

In a large non-stick or cast-iron skillet, heat approximately 1/4 cup of canola oil over medium heat. The oil is ready when a small piece of batter dropped into it sizzles immediately and browns within 10 seconds.

Working in batches, drop generous spoonfuls (about 1/4 cup each) of the potato mixture into the hot oil, flattening each mound gently with the back of the spoon to form patties approximately 3 inches wide. Fry for 3 to 4 minutes per side, or until the edges are crisp and golden brown.

Transfer the cooked latkes to a plate lined with paper towels to drain excess oil. Repeat with remaining batter, adding more oil as needed between batches. Serve immediately while hot with sour cream, applesauce, or both.