Heat butter in a medium sauce pan, until melted. Add flour and stir until smooth. Cook over medium heat until light golden brown, about 6 to 7 minutes. Meanwhile, heat the milk in separate pan until just about to boil.
Add warmed milk to butter mixture 1 cup at a time, whisking continuously until very smooth.
Bring mixture to a boil and continue cooking for 30 seconds. Remove pan from the heat. Season with salt and nutmeg pesto sauce makes about 1 cup 3 garlic cloves 2 cups lightly packed fresh basil leaves 3 tablespoons pine nuts generous pinch of kosher salt ½ cup plus 2 tablespoons extra-virgin olive oil ¼ cup parmigiano-reggiano cheese, freshly grated 3 tablespoons pecorino romano cheese, freshly grated. Drop garlic into a food processor with the motor running and process until chopped.
Add the basil, pine nuts, and salt. pulse until the basil and pine nuts are coarsely chopped continue processing until finely chopped. Drizzle in the olive oil with the motor running. Transfer to a small bowl and stir in the grated cheeses. *the pesto can be stored in a tightly sealed jar, topped with a thin layer of extra-virgin olive oil, for several weeks in the refrigerator.
Preheat the oven to 400°F. Bring about 6 quarts of water to a boil and add about 2 tablespoons salt (optional). Prepare a bowl of ice water. Trim the asparagus and boil for 1 minute.
Use tongs to remove the asparagus from the hot water reserve asparagus cooking water. Refresh asparagus in the ice bath for 30 seconds. Use tongs to transfer the asparagus to a colander, drain well, and cut each spear in half crosswise and set aside. heat olive oil over medium heat in a 12 to 14 inch sauté pan.
Add the eggplant and cook until golden brown and soft, about 5 minutes. Drain on a paper towel and set aside. cook the lasagne sheets in the same boiling water as the asparagus and cook for 2 minutes less than the package instructions. Drain and separate. prepare a 13x9 baking pan by coating with butter or cooking spray. layer 4 sheets of lasagne on the bottom of the pan top with 6 pieces of asparagus, 3 to 4 slices of eggplant and 3 tablespoons of besciamella sauce. top with 4 sheets of lasagne, asparagus and eggplant as above, and 3 tablespoons of pesto sauce. Repeat these 2 layers for a total of 4 layers.
End with 4 sheets of lasagne, remaining besciamella sauce and grated cheese. sprinkle with bread crumbs.
Place the baking pan on a baking sheet and bake for 20 to 25minutes, or until bubbling and golden brown on top.