How to Make It
Preheat oven to 475°F with racks in middle and lower third positions. Cook oil and garlic in a small saucepan over medium, undisturbed, until garlic begins to sizzle, 5 to 6 minutes. Remove from heat. Discard garlic.
Using tongs, toss together bell peppers, 1/4 cup of the garlic oil, 3/4 teaspoon of the salt, and 1/4 teaspoon of the black pepper on a baking sheet lined with parchment paper; spread in an even layer. Toss together mushrooms, 3/4 teaspoon of the salt, 1/4 teaspoon of the black pepper, and remaining 1/4 cup garlic oil on a separate baking sheet lined with parchment paper; spread in an even layer. Roast bell peppers and mushrooms in preheated oven until tender, about 22 minutes, rotating baking sheets between top and bottom racks halfway through cook time. Remove from oven; reduce oven temperature to 400°F.
While vegetables roast, whisk together ricotta, egg, parsley, 1 cup of the Parmesan, and remaining 3/4 teaspoon salt and 1/2 teaspoon black pepper in a medium bowl until smooth.
Spread 1/2 cup of the marinara sauce in bottom of a 13- x 9-inch glass or ceramic baking dish. Top with 3 lasagna noodles. Spread 2/3 cup ricotta mixture over noodles; top evenly with one third of the bell peppers and one third of the mushrooms. Top with 3/4 cup of the marinara. Starting with the 3 lasagna noodles, repeat layers twice.
Top final layer with remaining 4 lasagna noodles; spread with remaining 3/4 cup marinara. Arrange mozzarella slabs in a single layer on top. Sprinkle with remaining Parmesan (about 1 cup). Cover baking dish tightly with greased aluminum foil.
Bake at 400°F until mixture is bubbling (you will need to peek under foil to check), about 25 minutes. Remove foil; continue baking 10 minutes. Increase oven temperature to broil (do not remove lasagna from oven); broil until cheese is browned and bubbly, 3 to 5 minutes. Let stand 10 minutes. Sprinkle with basil; slice and serve.