1. The fava beans need to be blanched to make it easier to remove their skins; in a large pot, bring 6 cups water to a boil.
2. Add fava beans and blanch for about a minute, then use a slotted spoon to remove them to a cold water bath and slip off their skins; return water to a boil.
3. Now drop in the pasta with 1 tablespoon salt, stirring occasionally to prevent sticking, according to package directions.
4. Two minutes before pasta is done, drop in the fava beans and peas.
5. Meanwhile, in a small bowl, combine the egg yolks, cheese, and a little salt and pepper; set aside.
6. Once the pasta is al dente, drain, reserving 1/2 cup of the cooking liquid; return pasta and vegetables to the pot, add butter and stir.
7. Add egg mixture and chives, toss gently, and add a little cooking liquid (a tablespoon at a time) to form a silky sauce that clings to the pasta; adjust seasonings and serve with cheese for grating.