How to Make It
Preheat the oven to 350°. Spread the fideos on a rimmed baking sheet; bake for 8 minutes, or until lightly browned.
In a saucepan, combine the stock, wine, saffron and shrimp shells; bring to a boil. Remove from the heat, cover and let stand for 1 hour. Discard the shrimp shells.
In a large saucepan, heat 1 tablespoon of the oil. Add the chorizo and sliced garlic and cook over moderate heat until the garlic is golden. Add the pinch of red pepper, fideos and the shrimp stock and bring to a boil, stirring. Cook over moderate heat, stirring constantly, until the fideos are al dente and the sauce is creamy, 5 minutes. Stir in the shrimp and season with salt. Remove from the heat and let cool to room temperature. Stir in the egg whites and refrigerate for 1 hour.
Shape the mixture into twelve 3 1/2-inch cakes, about 1/2 inch thick. Set them on a baking sheet and refrigerate for 1 hour.
In a bowl, blend the mayonnaise, minced garlic and lemon juice. Whisk in 2 tablespoons of the oil and season with salt.
In a large cast-iron skillet, heat 1 tablespoon of the oil. Add 3 cakes and cook over moderately high heat until browned on the bottom, about 4 minutes. Turn the cakes, reduce the heat to moderate and cook until heated through, about 3 minutes longer. Transfer to a plate and keep warm. Repeat with the remaining oil and cakes. Top the fideo cakes with the garlic mayonnaise and serve warm.