Make a pile of flour on a work surface, and make a well in the center. Add eggs to the well, and scramble eggs with a fork, gradually incorporating flour from the edges. When the dough becomes too thick to use a fork, use a bench scraper to lift remaining dry flour over the top and begin to cut flour in until a shaggy dough forms.

Knead dough by hand until you have a smooth ball of dough, about 3 minutes. Cover and let rest for 10 to 15 minutes. Knead until a very smooth and elastic ball of dough forms, about 4 minutes more. Wrap tightly and rest dough in the refrigerator for at least 2 hours or up to overnight.

Add ricotta, Parmesan, egg yolk, parsley, salt, black pepper, and cayenne to a bowl, and stir together until evenly combined. Cover and refrigerate until needed.

Divide dough into 4 sections. Cover 3 sections with plastic, lightly flour a work surface, and shape the 4th into a rectangle. Use a rolling pin to roll dough into an 18x9-inch rectangle, thin enough to see your hand through.

Trim into 2 strips, approximately 18 by 4 1/2 inches. Maintain just enough flour on the work surface for this step and proceeding steps to prevent dough from sticking to the surface.

Transfer filling into a piping bag, or a plastic bag with 1 corner cut off, and pipe a 1/2-inch thick rope of filling lengthwise along each dough strip, 2 inches in from the edge. Mist each piece of dough very lightly with water.

Fold dough over filling, being careful not to trap any air bubbles. Press the 2 long edges of dough firmly together, flattening the seam to the thickness of a single layer of dough if possible. Use a fluted pasta cutter to trim excess dough to about 1/8-inch from the filling.

Starting at the end where the filling begins, use two fingers to pinch the filling and dough together very tightly every inch to inch and a half. Bend the pressed sections of dough between the filling forward slightly. Use the pasta cutter to slice between each to form individual agnolotti. It may be helpful to mist the dough again before doing this step.

Transfer finished agnolotti to a lightly floured, parchment-lined pan. Cover and refrigerate until ready to cook. Agnolotti can also be frozen on the pan before being transferred into freezer bags for storage.