1. Bring a large pot of water to a boil over high heat. Add the noodles and a generous pinch of salt and cook for half as long as the package suggests. Drain and float in cold water. (Skip this step if noodles are precooked.)

2. Preheat the oven to 350 degrees Fahrenheit. In a medium skillet over medium-high heat, fry the sausage links until cooked through, about 10 minutes. With kitchen scissors, cut the sausage into disks in the pan and continue to fry over low heat until the cut surfaces are crispy, about 20 minutes. Drain off the fat.

3. In a medium bowl, stir together the egg, ricotta, and 1/2 cup of the pecorino.

4. To assemble the lasagna, spread 1 cup of the tomato sauce in the bottom of a greased 9-by-13-inch baking dish. Drain and pat dry the noodles. Overlap one third of the noodles atop the sauce to cover the pan bottom. Spread all the cooked sausage over the noodles and spoon over another cup of sauce. Lay down the second third of noodles. Evenly dollop all the ricotta mixture on top of the noodles and flatten with the spoon to make an even layer. Top with the remaining noodles to completely cover the cheese. Pour over 1 1/2 to 2 cups sauce to cover. Evenly lay all the mozzarella slices on top. Sprinkle around the remaining 1/4 cup pecorino and drizzle with olive oil.

5. Bake uncovered for 40 minutes, or until the lasagna is bubbling all over and lightly golden on top. Let rest for 10 to 15 minutes before slicing. Serve with grated cheese and warmed extra sauce at the table.