These fresh ravioli get garnished with bright green fava beans and herbs.
Place chicken in a medium saucepan; cover with cold salted water. Bring to a boil; reduce heat to medium. Cook until breasts turn opaque, about 20 minutes.
Remove the chicken from the hot water, and set aside until cool enough to handle. Cut the cooked chicken breasts into fine dice, and set aside.
In a medium saute pan, melt 2 1/2 tablespoons butter over medium-low heat. Add the onion and garlic; cook until translucent, about 7 minutes. Remove saute pan from heat, and transfer mixture to a large bowl. Add the reserved chicken, prosciutto, tarragon, parsley, nutmeg, Parmesan, and whole egg. Season with salt and pepper; mix until combined. Set the filling aside.
Peel the skins from the fava beans, and set aside. Line a baking pan with parchment, and generously sprinkle parchment with cornmeal; set aside. Lightly flour a clean work surface. Divide the pasta dough into four equal balls, and cover each ball with plastic wrap.
Using a pasta machine, roll out one ball of dough, using as little additional flour as possible, to a transparent thickness (about #6 on the pasta machine). Place the rolled-out sheet on the floured surface, and cover with plastic wrap. Roll a second ball of dough into a sheet, and place next to the first one. Remove the plastic. Brush the egg white lightly and evenly over the first sheet of dough. Spoon 1/4 cup filling onto one end, with at least 1/2 inch dough around the edges; repeat, making five more mounds, spaced at least 1 inch apart. Carefully place the second sheet of pasta over the filling. Using your fingertips, press down, sealing both sheets of pasta all around the mounds. Using a pizza wheel or a sharp knife, cut the pasta into six individual squares, leaving a 1/2-inch border of pasta around the filling. Transfer the ravioloni to the prepared baking pan, and cover with a clean kitchen towel.
Repeat step five with the remaining two balls of pasta dough and the filling.
Bring one large stockpot and one small stockpot of salted water to a full boil. Place half of the ravioloni in the large stockpot, and cook until tender, about 5 minutes. Using a slotted spoon, transfer ravioloni to a colander to drain; set aside. Repeat with the remaining ravioloni.
Blanch the fava beans in the small stockpot of boiling water for 1 minute. Drain in a colander, and set aside.
Place the remaining 6 tablespoons butter in a medium skillet, and set over medium-high heat; cook until the butter bubbles and turns light brown. Divide the ravioloni among twelve serving plates, and drizzle with the browned butter. Garnish ravioloni with tarragon, parsley, ramp greens, if using, and the reserved blanched fava beans.