Preheat the oven to 500°F, line two shallow baking pans with foil and coat with nonstick spray.
Peel the tomatoes: Cut a small, thin slice from the bottom of each tomato, then cut them in half lengthwise and remove the core. Arrange cut side down on one of the prepared pans and using the tip of a sharp knife, score the skin of each tomato lengthwise. Place them in the oven for 4 to 5 minutes. You'll know when the tomatoes are ready to be peeled when you see the gap where you scored the skin widen slightly. Remove and reduce the oven temperature to 450°F. As soon as the tomatoes are cool enough to touch, peel them and remove the seeds. Chop into 1-inch pieces, transfer to a bowl and set aside.
Pre-cook the eggplant: Trim the ends from each eggplant, peel and cut lengthwise into 1/4-inch thick slices. If necessary, replace the foil on the pan you used for the tomatoes, or simply wipe off and re-coat with nonstick spray. Arrange the eggplant slices on the prepared pans, season lightly with salt and pepper and roast until tender, 12 to 15 minutes. Transfer the eggplant to a platter and set aside.
Pre-cook the zucchini: Trim the ends from the zucchini and cut them lengthwise into 1/4-inch thick slices. Re-coat the baking pans with nonstick spray, arrange the zucchini in a single layer and season lightly with salt and pepper. Roast until tender, 10 to 12 minutes. Transfer the zucchini to a platter and set aside. Reduce the oven temperature to 375°F.
Pre-cook the mushrooms and peppers: Place 2 tablespoons of the olive oil in a heavy skillet over medium-high heat. Add the mushrooms and sauté until they begin giving off liquid. Continue cooking for another minute, then add the red bell pepper and season the mixture with salt and pepper. Continue cooking until all the liquid has evaporated, the mushrooms are lightly browned and the peppers are tender. Transfer to a small bowl and set aside.
Prepare the fresh tomato sauce: Add the remaining 2 tablespoons of olive oil to the pan and add the onion. Sauté, stirring often, until the onion is soft and translucent, 4 to 5 minutes. Add the garlic and continue cooking just until fragrant, about 30 seconds longer. Stir in the tomatoes, lower the heat to medium and cook for 5 minutes. Season to taste with salt and pepper and continue cooking for another 15 minutes.
Prepare the cheese filling: Divide the fresh mozzarella in half. Cut one half into small (1/2-inch) cubes. Cut the other half into thin slices, then quarter each slice and set aside. Combine the ricotta, eggs and 1 cup of the shredded Asiago in a mixing bowl. Season with a little salt and pepper, then stir in the mozzarella cubes and parsley. Set aside.
Assemble the lasagna: Coat a 13 x 9-inch lasagna pan with nonstick spray, pour in the tomato sauce and tilt the pan to cover the bottom. Spread four lasagna noodles across pan, overlapping them on the long side by about 1/8-inch. Layer all the eggplant slices on top of the noodles, then spoon about 1/3 of the fresh tomato sauce over them. Add another layer of noodles, spread half of the ricotta mixture over them, then top with a third layer of noodles.
Arrange the zucchini slices over that layer and spoon another 1/3 of the fresh tomato sauce over them. Top with four more noodles, spread the remaining ricotta mixture over those, then add a final layer of noodles. Add the mushrooms and bell peppers to the remaining fresh tomato sauce and spread the mixture evenly over the top of the lasagna.
Bake the lasagna: Coat a piece of heavy duty foil with nonstick spray, cover the lasagna and bake for 1 hour. Remove the lasagna from the oven and uncover. Distribute the remaining fresh mozzarella and Asiago over the top and return to the oven for 15 minutes.
Allow to stand for at least 10 minutes before cutting.