Make the Puttanesca Sauce: Heat the olive oil in a large pot over medium-high heat. Add the onion and cook until soft and slightly caramelized, about 6 minutes. Add the garlic and cook for 2 minutes, stirring frequently. Add the tomatoes and the remaining ingredients and simmer until the sauce is thickened and slightly reduced, about 40 minutes. Adjust the seasoning to taste, cover, and set aside.
Make the Pesto Oil: Combine the garlic and basil in the bowl of a food processor or blender and process on high while adding the olive oil in a steady stream. Continue to process until well blended, season with salt to taste, and set aside until ready to assemble the lasagna.
Grill the vegetables: Light the grill or preheat the broiler. In a large shallow bowl, toss the zucchini, bell peppers, eggplants, and onions with the olive oil and salt. If using the broiler, arrange the vegetables in a single layer on 2 lightly greased or nonstick baking sheets. Grill or broil in batches, turning the vegetables once, until they are tender, lightly browned, and have released most of their moisture, 5 to 6 minutes per side.
Preheat the oven to 350?F and lightly grease a 9 x 13-inch baking dish.
Combine the ricotta cheese with 1/2 cup Pesto Oil in a medium bowl and set aside.
Spoon 1/2 cup of the Puttanesca Sauce onto the bottom of the prepared baking dish. Cover with a single layer of lasagna noodles, making sure they do not overlap. Top the lasagna with a layer of ricotta cheese, then a layer of grilled vegetables-eggplants, zucchini, onions, and bell peppers-a layer of grated mozzarella, and a layer of Puttanesca Sauce. Continue layering the lasagna, ricotta, vegetables, mozzarella, and sauce until all the ingredients have been used, ending with mozzarella.
Cover the lasagna with aluminum foil and bake for 45 minutes. Remove the foil and continue to bake until the lasagna is bubbling and golden brown, 15 to 30 minutes longer. Let the lasagna rest for 10 minutes before serving, drizzled with some of the remaining Pesto Oil.
Makes 8 to 10 servings