Cook lasagna according to package directions and lay them out on parchment paper in a single layer until ready to use.
Preheat oven to 350°F. Line a large cookie sheet with aluminum foil and set aside. In a 9x13 baking dish, spread just enough tomato sauce to cover the bottom. Set aside.
In a medium bowl, combine onion, garlic, zucchini and carrots with olive oil and toss to coat.
Spread in an even layer on prepared baking sheet and salt and pepper to taste. Bake for 15 minutes, then add mushrooms on top in an even layer, and bake for 10 more minutes.
In a medium bowl, combine 1 ½ cups mozzarella, ricotta, and Parmesan cheeses with parsley, red pepper flakes, egg and spinach. Salt and pepper to taste, and whisk to combine.
Spread an even layer of the cheese mixture onto each noodle, followed by a layer of diced tomatoes, then a layer of roasted veggies, and lastly a layer of tomato sauce (make sure to leave some sauce leftover - you'll need it later!).
Starting at one end, roll each noodle - you want it to be secure enough to keep the ingredients from spilling out the sides. Place each roll seam side down into the prepared baking dish.
Cover rolls with remaining tomato sauce (*all over* - you don't want the edges to get dry during baking) and cover with remaining mozzarella cheese.
Tent foil over the baking dish (without it touching the cheese) and bake for 25 minutes. Remove foil and bake another 10 minutes.