To Prepare Baked Lasagna Dish:
Preheat oven to 425 F. Bring 6 quarts water to boil and add 2 tablespoons salt. Set up ice bath next to boiling water.
Trim asparagus and boil one minute. Drain and refresh in ice bath. Remove, drain well, and cut into 4-inch to 5-inch pieces and set aside.
Cut pasta into 5-inch squares and drop into same boiling water as asparagus. Cook one minute until tender. Remove and refresh in ice bath. Drain on towels and set aside.
In a mixing bowl, stir balsamella, pesto, and grated cheese together until mixed well. Butter 4 gratin dishes and place one piece of 5-inch pasta on the bottom of each one. On top of pasta, place the following: 3 pieces of asparagus, followed by 2 tablespoons pesto, followed by another piece of pasta. Continue with this layering until you have 4 pieces of pasta and 4 layers of asparagus and pesto mixture. Lay one more piece of pasta on top, followed by a spoonful of pesto mixture and sprinkle each of the 4 gratin dishes with bread crumbs. Put all 4 dishes in oven and bake for 12 to 15 minutes, or until bubbling and golden brown on top. Remove and serve immediately.
In a large stone mortar, place pine nuts, basil, garlic and salt and grind with a pestle until paste. Add cheeses and drizzle in olive oil, beating with a wooden spoon. Store in jars, topped with extra virgin olive oil.