Preheat oven to 175°C. Arrange carrots and parsnips on a baking tray and arrange sliced onion and Roma tomatoes on another.
Dress each tray with half of olive oil, sugar, sherry vinegar, rosemary and thyme and season each tray lightly.
Toss vegetables gently and roast, uncovered until vegetables are cooked, about 35 minutes for carrots and parsnips and 50 minutes for onion and tomatoes.
Prepare cheese sauce while vegetables are roasting.
Bring milk up to a gentle simmer with garlic and nutmeg and keep warm. In a saucepot, melt butter and add flour, stirring constantly with a wooden spoon over medium heat until the aroma is mildly nutty, but mixture does not brown, about 3 minutes.
Ladle in a ½ cup of the warm milk while whisking, then repeat with another ½ cup while whisking. Keep ladling in milk until all has been added, then switch back to a wooden spoon and return to a simmer to thicken sauce. Season to taste and keep warm.
Stir ricotta in a bowl to soften and stir in ¼ cup Parmesan cheese. Pour one cup of sauce over ricotta and stir to combine. Return remaining sauce to low heat and stir in Asiago and Swiss Gruyere until melted. Keep warm, until vegetables have come out of the oven.
To assemble, keep oven at 175°C. Grease a 9-x-13-inch baking dish and spoon about 1/3 cup of cheese sauce on bottom of dish and top with lasagna sheets in a single layer, trimming if necessary. Spread an even layer of half of the mixed roasted vegetables over lasagna sheets and ladle about 1½ cups of cheese sauce over, topping with another layer of lasagna. Spread ricotta filling over lasagna and top with another single layer of pasta. Top with remaining vegetables, another 1½ cups of cheese sauce and a final layer of lasagna. Ladle remaining cheese sauce over pasta and sprinkle remaining ¼ cup Parmesan cheese on top.
Cover lasagna with parchment paper, then foil and bake for about 20 minutes. Remove foil and parchment and bake another 30 minutes, until bubbling and top has browned. Let lasagna sit for 15 minutes before slicing.
Lasagna can be made ahead, cut into squares and frozen, or recipe can be cut in half and prepared in a pie plate.