Preheat the oven to 450 degrees F.
Core and seed the peppers. Put on a sheet tray and roast until the skins are charred, about 2 to 3 minutes on each side. Transfer to a bowl and cover with plastic wrap. Let sit for 10 minutes then peel off the skin.
Preheat a grill pan or outdoor grill over medium high heat, and turn the oven down to 350 degrees F.
Slice the eggplant and squash lengthwise into 1/4-inch thick pieces. Arrange on a baking sheet and drizzle canola oil and balsamic vinegar over the top. Toss with salt and pepper, to taste. Put on the hot grill and cook for about 2 minutes on each side. Reserve 6 pieces of the grilled eggplant for Round 2 recipe Eggplant Rollatini.
In a small bowl combine the ricotta, egg, Italian seasoning, parsley, salt and pepper, to taste. Mix until well blended.
In a 9 by 9 baking dish put down a single layer of the grilled eggplant and top with 1 of the roasted bell peppers. Season each layer with a bit of salt and pepper. Spread 1/3 of ricotta mixture over top. Layer another single layer of eggplant followed by 1 piece of the grilled squash. Top with another 1/3 of the ricotta mixture (save remainder for Round 2 "Eggplant Rollatini") and a final layer of eggplant and remaining roasted pepper and yellow squash. Sprinkle with mozzarella cheese. Cover with aluminum foil and bake for 25 minutes, then remove the foil and bake until heated through and cheese is browned and bubbling, about 10 minutes more. Remove from the oven and allow to cool for 10 minutes.
Basil Walnut Pesto:
In the bowl of a food processer pulse together the basil, garlic, walnuts and Parmesan cheese. With the food processor running, slowly drizzle in the oil. Season with salt and pepper, to taste.
To serve, cut the lasagna into 4 squares. Serve topped with a generous spoonful of pesto.