Cook lasagna noodles according to package directions. Drain, cool slightly. Brush each side of noodle with olive oil so they don't stick together. Set aside.
Combine ricotta cheese and pesto in a small bowl, set aside.
Heat grill pan or grill to medium-high. In a medium bowl (or ziplock bag) drizzle cut zucchini, yellow squash, tomatoes and asparagus with olive oil to coat. Grill until vegetables are tender and grill marks are visible.Asparagus may take a little longer than other vegetable to cook. Cut asparagus into bite size pieces. Set vegetables aside.
If using fresh corn, cut corn off the cob and heat in a microwave safe bowl covered with plastic wrap until tender. Approx. 15-20 sec., set aside.
Shell fava beans by breaking the pod near the stem and pulling the string that runs down the middle of the pod. Beans are easily removed with your finger or a spoon. (usually 4-5 beans per pod). Fava beans have a slightly waxy looking layer which can be eaten just as is, if you prefer you can remove the waxy layer. Blanching the beans in hot water for approx. 30 sec. makes it very easy to remove the waxy layer.
Assemble the lasagna. Cut each lasagna noodle in thirds. Place one piece of noodle (1/3) on plate , spread a spoonful of ricotta/pesto mixture evenly on noodle. Add zucchini, squash, tomato, asparagus, corn, and fava beans. Sprinkle with basil. Repeat layering twice. Garnish the top layer of veggies with shaved or grated Parmesan cheese.