In a medium sauce pan, heat butter until melted. Add flour and stir until smooth. Over medium heat, cook until light golden brown, about 6 to 7 minutes.
Meanwhile, heat milk in separate pan until just about to boil. Add milk to butter mixture 1 cup at a time, whisking continuously until very smooth and bring to a boil. Cook 30 seconds and remove from heat. Season with salt and nutmeg and set aside. Yield: 2 cups
In a large pasta pot, combine 6 quarts of water, the lemon juice, 2 tablespoons salt, and a few peppercorns. Add the artichokes and cook until tender, about 12 minutes. Drain the artichokes and set aside.
Bring 6 quarts of water to a boil and add 2 tablespoons salt.
Make the pasta according to the recipe and roll it out on the thinnest setting on a pasta rolling machine. Cut the rolled pasta into pieces 10 inches long by 5 inches wide. Set up an ice bath with only a few ice cubes next to the stove top. Cook the pasta in the boiling water for 1 minute, drain and refresh in the ice bath. Remove the pasta from the ice bath and set aside on clean, damp kitchen towels.
Preheat the oven to 375 degrees F.
Butter a 12 by 9-inch casserole.
Cut the artichokes with a very sharp knife or a mandoline into 1/8-inch thick slices. Layer the lasagne, beginning with the besciamella, then a layer of pasta, then a layer of artichokes, each layer getting a sprinkling of pecorino. The top layer should be besciamella and cheese. Bake in the oven for 45 minutes. Allow to rest for 10 minutes before slicing and serving.
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 eggs and the olive oil. Using a fork, beat together the 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. Roll or shape as desired.