Put the onions through a food processor fitted with the grater attachment. Remove to a kitchen towel and squeeze out the excess liquid. Set aside.
Grate the potatoes in the food processor, then remove to a kitchen towel and squeeze out the excess liquid--for best results let sit over a colander for 30 minutes to dry out completely.
Add the potatoes to the onions. Then add the egg, 4 tablespoons flour, 1 teaspoon salt and 1/4 teaspoon pepper. Mix well to combine. Squeeze together a handful of the mixture; if the potatoes don't hold together, add more flour, 1 tablespoon at a time, until they do.
Heat 1 inch or so of oil in a large skillet over medium-high heat.
Use two soup spoons to form the pancakes. Scoop a heaping spoonful of the mixture onto one spoon and use the bottom of the other to pack the potatoes into the first spoon. Slide the formed potato pancakes into the hot oil, five or six at a time, being careful not to overcrowd the pan. Cook until golden brown on the bottom, about 3 minutes. With a spatula or tongs, flip the pancakes; cook the second side until golden, another 2 to 3 minutes.
Drain the pancakes on a paper-towel-lined baking sheet and season with salt. Hold in a warm oven until ready to serve.