Pulse the egg yolks, whole eggs, 3 cups flour and salt in a food processor until the dough comes together in a ball. Add more flour if the dough seems very sticky. Transfer the dough to a work surface and knead briefly until the dough is smooth. Gather into a disc, wrap in plastic wrap and let it rest for an hour at room temperature.

Bing a saucepan of water to a boil. Remove the beans from the pods, then drop them into the water to blanch for 2 minutes. Drain. When they're cool enough to handle, make a small tear on the tough outer skins and peel them off. You should have about 3 cups peeled fava beans.

Reserve ½ cup of the fava beans, and put the rest in a food processor along with the ricotta, grated cheese, parsley or basil and pepper. Puree to a thick, smooth consistency. Be sure to taste the mixture for salt as needed.

Divide the dough into 4 portions, keeping reserved dough covered while working so it doesn’t dry out. Flour the dough and roll into thin 3-inch wide sheets on a pasta machine (I stop at setting 6 on my hand-cranked Atlas). Trim the sheets into workable sections about 2 feet long and place on a lightly floured surface.

Scoop the fava filling into small balls about 1-inch in diameter and arrange 1-inch apart in the center of each pasta sheet. Make an egg wash with an egg white and a drop of water, and brush over the dough all around the filling. Fold dough lengthwise over the filling, pressing gently between each ravioli and pinching to seal along the open edge.

Cut the ravioli with a fluted cutter (or use a pizza cutter) Transfer the ravioli to a floured tray and refrigerate until ready to cook, about 4 hours ahead.

Heat the olive oil and butter in a skillet over medium heat. Sweat the leeks with a pinch of salt until soft. Add the asparagus, cover and cook 2 minutes, until tender but still bright green. Remove from heat and stir in the reserved fava beans.

Bring a large pot of salted water to a boil. Drop the ravioli in about 6 at a time and cook until they float to the surface, usually less than 3 minutes. Remove ravioli using a slotted spoon or mesh skimmer.

Transfer to a serving bowl and combine with the sauce. Serve right away with more grated cheese alongside.