Adjust the oven racks to the center and bottom positions. Preheat the oven to 450 degrees F. Spray two large baking sheets with oil.
Place the bell peppers, zucchini, mushrooms, fennel, onion, and garlic on the sheets and toss with the balsamic vinegar, olive oil, oregano, dried basil, salt, and pepper. Roast on the lower oven rack, stirring halfway through, until tender and slightly browned, 25 to 30 minutes. Remove the vegetables from the oven and reduce the oven temperature to 400 degrees F. You can chop the garlic If you want. Set the veggies aside.
In a medium bowl, combine the ricotta, Pecorino, and fresh basil.
In a 9 x1 3 x 3-inch freezer to oven-proof baking dish, spread ½ cup marinara on the bottom of the dish. Arrange 3 lasagna noodles across the dish (they will expand when they cook).
Top with ¾ cup sauce, one-fourth of the roasted vegetables (and garlic), one-fourth of the ricotta cheese mixture, and ½ cup mozzarella.
Repeat 3 more times, starting with the pasta. Arrange the last 3 sheets of pasta noodles on top and spread with the remaining marinara sauce.
Cover with foil and bake on the center rack until the lasagna is cooked through in the center, about 45 minutes. Uncover and cook until bubbling hot, about 10 minutes more. Add the remaining mozzarella and bake until melted, about 5 minutes. Remove from the oven and let rest for 15 minutes before serving. Cut into 8 squares and serve.