Peel the onions and chop finely. Brown in oil. Add tomato juice, vegetable broth, salt, and pepper and bring to a simmer for 10 minutes. Pluck the basil and add half of it to the sauce. Add 1 liter (approximately 4 cups) of milk to the sauce. Mix the remaining mix with the flour and add to the sauce. Bring to a boil.
Rinse the asparagus, peel the lower third and cut into 2 cm (approximately 1 inch) chunks.
Add asparagus and thawed vegetables into the sauce. Season with salt and pepper. Place 1/6 of the vegetable sauce into the greased lasagna pan. Distribute 3 sheets on top of the sauce. Continue to layer sauce with noodles, ending with the sauce on top. Sprinkle with Parmesan and bake in an oven at 200°C (approximately 400°F) for about 35 minutes.
To serve: Cut into slice and keep warm. Garnish with remaining basil leaves.