Bring the salted water to a boil.
Meanwhile, prepare the leeks: Cut off and discard the top third of the rough green portion and the root ends. Remove any brown or wilted outer layers. Slice the remaining green and white parts into 1/2-inch thick rounds. Rinse the leek slices in several changes of cold water, swishing them around to remove all soil and grit.
In a large skillet, heat the olive oil over medium heat. Crumble the sausage meat into the skillet and cook, breaking up the lumps, until golden, about 5 minutes. Add the leeks to the skillet and cook, stirring, until wilted, about 5 minutes. Stir in the shallots and cook for 1 minute. Add 1 tablespoon of the butter, the peas, and stock. Heat to a boil, reduce the heat to medium-low, and simmer gently for 5 minutes. Season with salt and pepper, cover the skillet, and set aside.
Meanwhile, stir the bow ties into the boiling water. When the water returns to a boil, uncover the pot. Cook the pasta, stirring occasionally, until al dente -- tender, but firm -- about 12 minutes. Drain the bow ties well and return them to a pot over low heat.
Add the sausage and leek sauce to the pasta and toss well until the pasta is coated. Remove the pot from the heat, add the remaining 1 tablespoon butter and the grated cheese, and toss well. Transfer to a warmed serving platter or individual bowls. Serve immediately, passing additional grated cheese on the side, if you like.
Courtesy of Lidia's Italian Table by Lidia Matticchio Bastianich