The vegetables in this meatless lasagne can be prepared a day ahead, covered, and stored in the refrigerator.
Preheat the oven to 450°F. Place in a large bowl:
Add to the vegetables and toss to coat:
Divide the vegetables between 2 rimmed baking sheets, spreading them in a single layer. Roast for 20 minutes. Toss the vegetables with a spatula and continue to roast until well browned and soft, about 20 minutes more. Meanwhile, prepare or have ready:
Reduce the oven temperature to 375°F. Grease a deep 13 × 9-inch baking dish, 13 × 9 × 2-inch baking pan, or lasagne pan. Have ready:
For dried noodles, cook in a large pot of boiling salted water until barely tender. Drain the pasta, rinse under cool water, and blot it dry. For fresh lasagna noodles, do not boil. Peel and chop the roasted garlic cloves. Prepare:
Mix the chopped garlic into the filling. Spread a thin layer of tomato sauce over the bottom of the prepared pan. Cover with a layer of pasta, slightly overlapping. Spread with one-third of the cheese filling. Spoon one-third of the roasted vegetables on top, then sprinkle one-quarter of the mozzarella and Parmesan over the ricotta. Top with ½ cup sauce. Add another layer of pasta and continue layering the lasagna until you have 4 layers of pasta and 3 layers of filling. Spread the remaining sauce on top and sprinkle with the remaining mozzarella and Parmesan. Place the pan on a baking sheet to catch any drips, loosely cover the pan with foil, and bake for 30 minutes. Uncover and continue to bake until golden and bubbling, 20 to 25 minutes more. Let stand for 15 minutes before serving.