To prepare each type of latke, grate the vegetables and combine with eggs and salt. Heat oil in a large skillet and fry latkes until crisp on both sides.

Heat one tablespoon oil in a large skillet over medium heat. Sauté onion until golden. Season with black pepper.

Place egg and remaining cup of oil in a tall container, wide enough to fit the head of your immersion blender. Place immersion blender directly over the egg yolk and pulse slowly until thick and creamy.

Add lemon juice, sugar, salt, and onions. Mix to combine.