Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes for dried pasta or 2 to 3 minutes for fresh pasta. Drain pasta.
**If using eggplant, skip the above step. Instead, slice the eggplant lengthwise into very thin sheets. Try to slice them as thin as possible. Use the eggplant slices in place of noodles for the remainder of the recipe.
In a food processor combine the sun-dried tomatoes and basil. Pulse until the mixture is combined. Transfer to a small bowl. Stir in 1/4 cup Parmesan. Set aside.
In a large skillet , add 1/2 tablespoon olive oil, onion, and garlic and cook until tender, about 4 minutes. Add asparagus and cook until tender, about 4 minutes. Transfer the mixture to a large bowl. Add the ricotta, salt, and pepper and stir to combine.
Preheat the oven to 350 degrees F. In a 9 by 13-inch baking dish sprinkle some of the sun-dried tomato mixture on the bottom of the casserole dish. Place some lasagna (or eggplant)sheets, then half asparagus mixture. Next sprinkle some mozzarella cheese and some of the remaining Parmesan. Continue for 1 more layer. Top with lasagna (or eggplant) sheets, some sun-dried tomato mixture, mozzarella, and Parmesan. Bake until the ingredients are warm and the cheese is melted, about 25-30 minutes.
Original recipe for Asparagus Lasagna by Giada De Laurentiis can be found on www.foodnetwork.com.