Start by cracking the eggs into a bowl and beating them with a pinch of salt and the grated Pecorino. Using a coarse grater, grate the raw potatoes and add them to the eggs. Mix thoroughly to combine the ingredients.
Spread the potato mixture evenly over an approximately 20x30 cm baking sheet lined with parchment paper. Smooth the surface and bake in a preheated oven at 180°C (350°F) for 30 minutes.
Lay a sufficiently large sheet of parchment paper on your work surface and transfer the freshly baked potato base onto it. Cut the mozzarella into slices and then into strips. Arrange the slices of prosciutto side by side over the potato base, overlapping them slightly, then distribute the mozzarella strips evenly on top.
Starting from the long side of the rectangle and using the parchment paper to help you, roll the base tightly around the filling to form a compact roll. Twist the parchment paper at both ends to seal it tightly, like a candy wrapper.
Gently transfer the wrapped roll back to a baking sheet. Bake for an additional 5 minutes until lightly golden, then remove from the oven. Let it rest for about 15 minutes before slicing and serving so it can set and hold its shape.