Squash Filling

1. Roast butternut halves cut-side down at 400°F until collapsing, ~50 min. Scoop, pass through fine-mesh sieve, and dry the purée in a sauté pan until it holds a peak — wet filling blows out agnolotti.
2. Fold purée with mascarpone, half the Parmigiano, nutmeg, salt. Cover in a shallow container and refrigerate promptly. Refrigerate filling in a shallow container within 2 hours and chill before filling pasta.

Pasta Dough and Assembly

1. Make pasta: flour, eggs, yolks; knead 8–10 min to a smooth, tight dough. Rest wrapped 30 min minimum.
2. Roll the dough with a pasta machine to thin sheets that are just short of translucent; settings vary by machine. Put filling into a piping bag or zip-top bag with a corner snipped off. Pipe a narrow line along the dough, fold the dough over the filling, pinch it into small parcels, and cut between the pinches with a pasta wheel. Arrange on baking sheets lightly dusted with some of the listed flour, single layer. Refrigerate at or below 40°F; use within 24 hours or freeze.

Brown Butter, Cooking, and Serving

1. Melt the butter in a large skillet over medium heat. Swirl until the milk solids are golden and smell nutty. Remove from heat and add the sage leaves. Cook the pasta in batches if needed so it can be tossed gently without crowding.
2. Blanch agnolotti in aggressively salted water 2–3 min until they float and the plin is tender. Transfer straight to the brown butter with a splash of pasta water; toss to emulsify and glaze.
3. Plate, rain Parmigiano and crushed amaretti over the top.