Step 1

In a 2-cup liquid measuring cup or medium bowl, whisk the eggs and yolks, ¾ cup water and 1 tablespoon of the oil. In a food processor, process the Parmesan chunks until finely ground, about 20 seconds. Add the panko, ¼ teaspoon of nutmeg, 1/2 teaspoon salt and ½ teaspoon pepper. Process until the mixture is powdery, about 30 seconds. With the machine running, add the egg mixture, then process until smooth, about 1 minute. Let rest in the food processor for 5 minutes; the mixture will thicken as it stands.

Step 2

Process for another 10 seconds. The mixture will be thick but smooth and resemble mashed potatoes. Scrape it into a medium bowl, cover with plastic wrap and let rest at room temperature for 15 minutes or refrigerate for up to 1 hour; the mixture will thicken further as it stands.

Step 3

Line a rimmed baking sheet with kitchen parchment and brush the parchment with the remaining 2 tablespoons oil; set aside. In a large pot over medium-high, bring the broth to a boil. Transfer one-third of the dough to the hopper of a ricer with 3/16-inch perforations. Press the dough directly over the pot of simmering broth until it forms rough 3-inch lengths, then shake the ricer to release the dough into the broth. Repeat with the dough remaining in the ricer. (Alternatively, place a rack with a ⅜-inch wire grid across the pot of simmering broth. Scoop one-third of the dough onto the center of the rack, then use a silicone spatula to press the dough through the wires, allowing the dumplings to fall into the broth; rap the rack to release the last bits of dough into the pot.)

Step 4

Cook the passatelli until it floats to the surface, then continue to cook for 1 minute. Using a slotted spoon, scoop out the passatelli, letting it drain, then transfer to the prepared baking sheet. Cook the remaining dough in two more batches in the same way, then remove the pot from the heat. Let the passatelli rest for 15 minutes, stirring occasionally to help it cool; it will firm up as it cools.

Step 5

Return the broth to a simmer over medium-high, then taste and season with salt and pepper. Divide the passatelli among individual bowls and ladle in the broth. Top each serving with shaved Parmesan and grated nutmeg, then drizzle with oil.