Preheat oven to 425°
Pulse mushrooms, carrots, and broccoli in food processor until finely chopped.
Heat a large skillet over medium-high heat. Add olive oil to pan and swirl to coat.
Add onion to pan and saute about 4 minutes. Now add mushrooms carrots and broccoli to pan. Saute another 5-7 minutes until slightly golden.
Mix in minced garlic, salt and pepper and saute another 2 minutes. Remove from heat.
Heat 4 cups of non-dairy milk in medium saucepan over medium heat with Italian seasoning and nutritional yeast. Bring to boil and remove from heat.
Mix 1/3 cup of water with flour in small bowl. Return pan back to medium heat and slowly whisk in flour mixture until blended. Bring to a boil; reduce heat and simmer for approx. 5 minutes, constantly stirring. Remove from heat and stir in salt and pepper.
Coat your 13 x 9 ceramic or glass baking dish and spread 1/3 cup of milk mixture on bottom of dish.
Arrange 3 noodles over the milk mixture, spread vegetable mixture over noodles and pour 1/2 cup of milk mixture over vegetables. Repeat layers, ending with noodles. Pour your remaining milk mixture on top over noodles.
Bake at 425° for 30 minutes. After 30 minutes, if you would like to top with vegan cheese, sprinkle 1/4 cup over top and broil for 2 minutes until light golden brown.
Enjoy!