Peel the potatoes and grate them finely into a mixing bowl along with the yellow onion.
Remove excess moisture from the grated mixture by draining any liquid that collects.
Combine the grated potatoes and onion with salt, black pepper, flour, and the egg; mix thoroughly with your hands to form a sticky batter.
Warm 1 to 2 tablespoons of vegetable oil in a skillet over medium heat.
Drop rounded spoonfuls of batter into the pan and gently press them flat.
Cook the pancakes for approximately 3 to 4 minutes on each side until golden and crisp, then transfer them to a paper towel to drain.
Fry the pancakes once more briefly, about 30 to 60 seconds per side, to achieve an extra crunchy texture.
Serve immediately while hot, with toppings like applesauce or sour cream if desired.
