To assemble the lasagna, beat the eggs in a medium bowl until
smooth. Add ricotta and fresh basil and whisk thoroughly. Boil the
pasta, two pieces at a time, until al dente, then let cool slightly on a
baking sheet. Cover the bottom of a baking dish with about 1 cup of
sauce. Arrange two pieces of cooked pasta on top, and pour in the
ricotta mixture. Arrange two more pieces of pasta, then the meat
mixture, 1 cup parmesan, ½ cup pecorino and enough sauce to cover
the meat. Top with another layer each of pasta, vegetables, cheese
and sauce. Add the final layer of pasta and top with the remaining
sauce and cheese. Grease a piece of foil with cooking spray and
lightly cover the dish. Bake for 40 minutes, covered, then remove
foil and bake an additional 15 minutes until cheese is melted. Cool
for 20 minutes before serving.
