Make a mound with flour on a clean counter, create a well in the center, crack 3 whole eggs into well, and incorporate flour gradually with a fork until shaggy dough forms. Knead by hand for 8 minutes until smooth and elastic, wrap in plastic, rest 20 minutes at room temperature.
Mix ricotta, Parmigiano-Reggiano, prosciutto, 1/4 tsp freshly grated nutmeg, and black pepper in a bowl until combined. Taste and adjust seasoning. Set filling aside.
Roll pasta dough through a pasta machine, starting at setting 1 and progressing to setting 6 or 7 until thin enough to see your hand through it. Lay sheet on a lightly floured surface. Cut 2-inch squares using a fluted pastry wheel or knife, spacing evenly.
Place 1/2 teaspoon filling in the center of each square. Brush edges with egg wash made from 1 egg yolk mixed with 1 tbsp water. Fold square diagonally to form triangle, press edges firmly to seal. Wrap each triangle around your index finger, bringing the two pointed corners together, press and pinch to seal into the signature cappelletti hat shape.
Bring a large pot of water to a rolling boil, add 2 tbsp kosher salt. Working in batches to avoid crowding, add cappelletti and cook for 3-4 minutes until they float to the surface and remain there for 30 seconds. Remove with a slotted spoon to a warm bowl.
In a large skillet, melt 4 tbsp unsalted butter over medium heat. Add minced garlic and cook for 30 seconds until fragrant. Add 8 whole sage leaves and crispy pancetta, cooking for 1 minute until sage becomes fragrant and pancetta releases its flavor.
Gently toss cooked cappelletti into the sage-brown butter sauce, add 1/4 tsp freshly grated nutmeg, and toss gently to coat, cooking for 1 minute. Transfer to warm bowls, spoon sauce and pancetta over each serving, finish with additional grated Parmigiano-Reggiano and cracked black pepper. Serve immediately.
Inspired by Rachelle Murphy’s winning cappelletti. This is a plausible recreation, not the chef’s original recipe.