Combine eggs and spinach. Mound 3 1/2 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the egg and spinach mixture and the olive oil. Using a fork, beat together the spinach, eggs and oil and begin to incorporate the flour, starting with the inner rim of the well.

As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.

Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Divide the dough into 3 equal portions and roll each out to the thinnest setting on a pasta rolling machine.

Bring about 6 quarts of water to a boil and add 2 tablespoons salt. Set up an ice bath next to the stove top. Cut the pasta into 20 (5-inch) squares and drop into the boiling water. Cook 1 minute, until tender. Drain well and refresh in the ice bath. Drain on towels and set aside.

Preheat the oven to 375 degrees F. In a brownie pan, assemble the lasagne, beginning with a layer of ragu, a sprinkling of grated Parmigiano, a layer of pasta, a layer of bechamel, a layer of ragu, a sprinkling of grated Parmigiano etc. until all sauce and pasta are used up. The top layer should be pasta with bechamel over it. Top the lasagne with grated Parmigiano-Reggiano and bake in the oven for 30 to 45 minutes, until the edges are browned and the sauces are bubbling. Remove and allow to cool for 10 minutes before slicing.