1. Preheat the oven to 400° and line a large rimmed baking sheet with foil. Steam the potatoes over boiling water until just tender, 10 to 12 minutes. Transfer to a plate to cool slightly.
2. Strain the beaten eggs into a soup plate and season lightly with salt. In another soup plate, combine the Parmesan with the cayenne. Working in small batches, coat the potatoes with the beaten egg, shaking off the excess, then toss them in the Parmesan mixture. Set the potatoes on the baking sheet and roast for about 25 minutes, or until golden. Serve hot or at room temperature.
Make Ahead: The potatoes can be kept at room temperature for 3 hours.
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