In a medium bowl, whisk together the whole eggs and egg yolks until just combined.
Stir in the grated Parmesan, bread crumbs, nutmeg, and a generous pinch of salt and pepper.
Mix with a fork until a soft, slightly sticky dough forms.
Cover the bowl and refrigerate the dough for at least 30 minutes, or up to 24 hours. This allows the bread crumbs to hydrate and the dough to firm up, which is crucial.
When ready to cook, pour the vegetable stock into a large pot and bring it to a boil.
Reduce the heat to maintain a gentle, steady simmer.
Working in batches, place a portion of the chilled dough into a potato ricer fitted with the large-hole disk.
Hold the ricer over the simmering stock and press the dough through. As the passatelli emerge, cut them into 2- to 3-inch lengths with a knife or scissors, letting them drop directly into the stock.
Cook for just 2-3 minutes, or until the passatelli float to the surface. They cook very quickly.
Taste the broth and adjust seasoning with salt and pepper if needed. Ladle the passatelli and broth into warm bowls and serve immediately.
Do not let the broth boil vigorously when cooking the passatelli. A gentle simmer is key to preventing them from breaking apart.