1. Place the eggplant, squash, and zucchini on a baking tray and brush them on both sides with some of the olive oil. Lightly season them with salt and pepper.

2. Set up a barbecue grill and preheat it to medium.

3. Grill the eggplant until just soft, 2½ to 4 minutes per side. Transfer the grilled eggplant to a wire rack to cool. Leave the grill burning.

4. Grill the squash and zucchini until just soft, about 2 minutes per side. Transfer the grilled squash and zucchini to the wire rack with the eggplant to cool. Leave the grill burning.

5. Place the bell peppers on the grill and cook, turning frequently, until the skin is just charred black, about 10 minutes. Transfer the bell peppers to a paper bag, close it tightly, and let the peppers steam for about 5 minutes. Remove the peppers from the bag and, when they are cool enough to handle, pull off the charred skin. Discard the skin, seeds, and stems and cut the roasted peppers into long, 1-inch-wide strips.

6. Bring a large pot of salted water to a boil over high heat. Add the lasagna noodles and cook according to the package directions until just tender. Do not undercook the lasagna noodles because they will not continue to cook in the oven. Drain the noodles well and lay them out flat on a clean dish towel (not terry cloth) so they do not stick together.

7. Place ¾ cup of the Parmesan cheese and the ricotta cheese, eggs, basil, and parsley in a small bowl. Add ½ teaspoon each of salt and pepper and stir well to combine.

8. Position a rack in the center of the oven and preheat the oven to 375°F.

9. Brush a 9 by 13–inch baking pan lightly with ¼ to ½ cup of the marinara sauce. Arrange one fourth of the lasagna noodles in a single layer over the marinara sauce, trimming them to fit if necessary. Arrange half of the eggplant slices over the noodles. Spread half of the ricotta mixture evenly over the eggplant and sprinkle a third of the mozzarella on top.

10. Arrange a third of the remaining lasagna noodles over the mozzarella. Spread about ½ to ¾ cup of the marinara sauce over the pasta (the lasagna will hold together better and be easier to serve if you use thin layers of marinara sauce). Cover the sauce with a layer each of the squash, zucchini, and red peppers, using them all up. Spread the remaining ricotta mixture over the vegetables and top this with half of the remaining mozzarella.

11. Arrange half of the remaining lasagna noodles over the mozzarella and cover them with the remaining eggplant. Brush the eggplant with the pesto and sprinkle the remaining mozzarella on top.

12. Arrange the remaining lasagna noodles over the mozzarella. Spread about 1 cup of the marinara sauce over the noodles so they are completely covered and sprinkle the remaining ½ cup of Parmesan cheese on top.

13. Bake the lasagna until it is hot and bubbly, about 1 hour. Remove the pan from the oven and let the lasagna rest for at least 15 minutes before cutting it. Heat the remaining marinara sauce (about 2 cups) in a small saucepan over medium heat. Slice the lasagna and serve it while still hot, with the remaining marinara sauce on the side.