To prepare roasted vegetables: In a large mixing bowl, toss vegetables with olive oil, garlic, salt and pepper. In an even layer, arrange vegetables on a large nonstick baking sheet lined with parchment paper. Roast for 15 minutes or until tender, stirring halfway through. Remove from heat.
To prepare filling: In a separate bowl, combine ricotta, Romano and parsley. Mix in eggs. Salt and pepper to taste.Reduce oven to 350˚F.
Spread 1/3 jar of marinara sauce over the bottom of 13" x 9" baking dish. Place lasagna sheets over sauce, overlapping to fit. Dollop with ricotta mixture and goat cheese. (Do not spread.) Layer with roasted vegetables. Evenly sprinkle with 1/3 of the shredded provolone. Spoon another 1/3 of marinara sauce over cheese, using spatula to cover. Repeat layering: lasagna noodles, dollops of ricotta mixture and goat cheese, roasted vegetables and shredded cheese.
Top with remaining lasagna sheets,1/3 of marinara sauce, 1/3 of shredded provolone and the grated Parmesan.
Cover dish with foil and bake for 45 minutes. Uncover and bake for another 10 minutes, or until cheese is hot and bubbly.