Preheat the oven to 425°F (220°C) and line three baking sheets with parchment paper.
Place the grape tomatoes on one parchment-lined sheet, leaving them whole; spread the sliced mushrooms, broccoli florets, chopped onion, chopped red and orange bell peppers, and chopped zucchini across the other two sheets without crowding.
Drizzle the vegetables and tomatoes with the olive oil, season with salt and pepper, and toss each sheet so everything is evenly coated.
Roast the vegetables and tomatoes for 25–30 minutes, until the tomatoes are bursting and the other vegetables are tender and lightly browned. Remove from the oven and let cool slightly.
In a mixing bowl, combine the ricotta, grated parmesan, dried basil, dried oregano, 1/4 teaspoon salt, and 1/4 teaspoon pepper; stir until smooth.
Tear or roughly chop the roasted vegetables (except keep some whole roasted tomatoes aside for topping) and mix the grated provolone and mozzarella together; reserve some cheese and tomatoes for the final topping.
Spray a 9x13-inch baking dish with nonstick spray and spread about 1/2 cup marinara sauce over the bottom.
Place 3 no-boil lasagna noodles over the sauce to form the first layer. Spread one third of the roasted vegetables over the noodles, drop spoonfuls of one third of the ricotta mixture across the vegetables, pull apart one burrata ball and scatter pieces evenly over the layer, then sprinkle with a portion of the grated provolone/mozzarella mixture. Spoon a little marinara over the cheese.
Repeat the layering two more times: 3 noodles, one third of the roasted vegetables, ricotta mixture, torn burrata, grated cheeses, and a little marinara each time.
Finish with a final top layer of noodles, spread the remaining marinara over the top, sprinkle with the remaining grated cheeses, and arrange the reserved roasted cherry tomatoes on top.
Place the assembled lasagna on a large baking sheet, reduce the oven temperature to 400°F (200°C), and bake for 45 minutes.
Remove the lasagna from the oven and let it rest undisturbed for 45–60 minutes before slicing and serving.
