Preheat the oven to 475 degrees F, or preheat the broiler.
Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a 12 to 14-inch frying pan, heat the butter over medium-high heat until it foams and subsides. Add the prosciutto and peas and cook over high heat until the meat is browned and the peas are tender and cooked through, about 5 minutes. Season with salt and pepper and remove from the heat.
Cook the tagliolini in the boiling water until tender and not quite cooked through, about 1 minute. Drain well and toss in the pan with the peas and prosciutto. Add the besciamella and toss over high heat for 30 seconds, then transfer to an ovenproof casserole. Top with the grated Parmigiano and cook in the oven or broiler for 3 to 5 minutes, until the cheese is browned and besciamella bubbles. Serve immediately.
Mound 3 1/2 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the eggs and the olive oil. Using a fork, beat together the eggs and oil and begin to incorporate the flour, starting with the inner rim of the well.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature.
Roll the pasta out on a pasta rolling machine to the desired thickness.
In a medium saucepan, heat butter until melted. Add flour and stir until smooth. Over medium heat, cook until light golden brown, about 6 to 7 minutes.
Meanwhile, heat milk in separate pan until just about to boil. Add milk to butter mixture 1 cup at a time, whisking continuously until very smooth and bring to a boil. Cook 10 minutes and remove from heat. Season with salt and nutmeg and set aside.
Recipe copyright 2001, Mario Batali. All Rights Reserved.