In a large pot of boiling water, cook noodles until barely tender.
Drain and rinse under cold water.
Spread the noodles on clean kitchen towels, cover with plastic wrap and set aside.
In a small bowl, combine sun-dried tomatoes and dried porcini mushrooms.
Add 1 cup boiling water, cover and let stand for 10 minutes.
Lift out the tomatoes andamp; mushrooms and chop.
Strain the soaking liquid through a fine sieve and set aside.
In a saucepan, heat 1 cup of the milk over medium heat.
Meanwhile, put 3 tablespoons of flour in a small bowl and gradually whisk in the remaining 1/3 cup of milk until smooth; whisk into the hot milk and stir constantly over the heat until the sauce comes to a simmer and thickens.
Continue cooking and stirring for 1 minute.
Remove from heat.
Whisk in the cream cheese, then 2/3 cup of the spaghetti sauce and the vinegar.
Searson with salt and pepper. Set aside.
In a large non-stick skillet, heat oil over medium-high heat.
Add onions, carrots and garlic and sauté until soft, about 2 minutes.
Add fresh mushrooms, rosemary, and the reserved tomatoes and porcini; cook until the fresh mushrooms are just wilted, about 2 minutes longer.
Stir in the remaining 1 teaspoon of flour.
Add the reserved soalking liquid and the remaining 1/3 cup of spaghetti sauce.
Cook until the mixture thickens, about 1 minute.
Remove from heat, season with salt and pepper.
Lightly spray a 9x13 in baking sheet with cooking spray or oil.
Line bottom with 1/4 of noodles (1 layer).
Then spread 1/2 of mushroom mixuture and sprinkle with 2 tablespoons parmesan.
Add 2nd layer of noodles, then the squash (sprinkle with salt and pepper) and another 1/2 cup of the sauce.
Add 3rd noodle layer, remaining mushroom mixure and 2 tablespoons of parmesan.
Top with remaining noodles and sauce, then remaining parmesan.
Lightly oil a large piece of aluminum foil.
Bake the lasagne for 30 minutes, uncover and bake for additional 10 to 15 minutes or until lightly brown and bubbing.
