Start by peeling the potatoes and grating them using a box grater or a food processor fitted with a grating attachment. Place the grated potatoes in a large bowl of cold water to prevent them from turning brown.
Grate the onion and add it to the bowl with the potatoes. Mix well to combine.
Drain the potato and onion mixture using a colander, pressing down to remove as much liquid as possible. This will help ensure that your latkes turn out crispy.
Transfer the drained mixture to a clean kitchen towel or cheesecloth and squeeze out any remaining liquid.
Place the drained potato and onion mixture back into the bowl and add the beaten eggs, flour, salt, and pepper. Mix well until all the ingredients are evenly combined.
In a large skillet, heat about 1/4 inch of vegetable oil over medium-high heat. Make sure the oil is hot before adding the latkes to the pan.
Using a spoon or your hands, take a small amount of the potato mixture and flatten it into a pancake shape. Carefully place it into the hot oil and repeat with the remaining mixture, making sure not to overcrowd the pan.
Fry the latkes for about 3-4 minutes on each side or until they are golden brown and crispy. Once cooked, transfer them to a paper towel-lined plate to remove any excess oil.
Repeat the frying process with the remaining potato mixture until all the latkes are cooked.
Serve the potato latkes hot with your choice of traditional accompaniments or as a side dish with sour cream or applesauce.