Meanwhile, place the eggs in a small bowl and beat to blend. Stir in the cheese and a lots of freshly ground pepper. Set aside.
Bring a large pot of salted water to a boil. Add the pasta and cook until tender but firm to the bite, 9 to 11 minutes. Reserve 1 cup of cooking water, then drain, leaving a little water clinging to the pasta.
Add the pasta to the skillet with the sausage meat (still simmering gently, or reheated) and toss to thoroughly and evenly coat the pasta. Turn the heat to very low (or you will scramble the eggs) and very quickly stir in the egg mixture and toss until each piece of pasta is evenly coated with sauce. Add a bit of the reserved pasta water until you have a smooth sauce. Serve immediately.
Pass the pepper mill and additional freshly grated Parmigiano-Reggiano.