1. Preheat the oven to 350 degrees. Cook the lasagna noodles according to package directions. Drain, rinse and set aside. Reserve 1 tablespoon pasta water.
2. Heat 1 tablespoon of the oil in a medium pot over medium-low heat. Add the garlic; cook 2 minutes. Add the tomatoes; cook 15 minutes. Whisk in 1 tablespoon of the goat cheese until combined. Set aside.
3. Meanwhile, heat 2 tablespoons oil in a 12-inch skillet over medium heat. Add the onion; saute 3 minutes. Add the leek; cook 3 minutes. Add the mushrooms; cook 10 minutes. Add the asparagus; cook 3 minutes.
4. Turn heat off; add 1 1/2 tablespoons goat cheese and the mozzarella, reserved pasta water, nutmeg, salt and black pepper. Add the mint and basil, reserving 1 teaspoon of each.
5. Spread 1/2 cup tomato sauce on the bottom of a baking dish. Spoon 1/2 cup vegetable mixture onto each noodle, roll up and place seam side down in baking dish. Drizzle with remaining tomato sauce; crumble remaining goat cheese on top. Bake 15 minutes. Remove from oven, sprinkle with the Parmesan and reserved mint and basil; serve.