Preheat oven to 350 degrees Fahrenheit. Grease a 9 x 13 inch baking dish with cooking spray.
Bring a large pot of lightly salted water to a boil. Place pasta in the pot, cook for 8 to 10 minutes, until al dente, and drain. Meanwhile…
Heat 2 tsp olive oil in a large saucepan over medium heat. Stir in the mushrooms, chopped red bell peppers and cook 5-10 minutes, until all liquid from the vegetables is released.
Add the spinach, garlic, and chopped broccoli and mix until incorporated, about 2 minutes. Remove the veggies into a bowl.
Melt 4 tbs butter in the saucepan over medium heat. Mix in 4 tbs flour, and stir continuously until a thick paste forms (this is a roux, and will serve as a base to thicken the milk to make your cheese sauce).
Carefully pour in the milk a quarter of a cup at a time, mixing continuously, waiting until it each quarter cup is fully incorporated until adding the next quarter cup. Once all of the milk is added, keep stirring until thickened and there are no lumps.
Stir in the 2 cups of cheese, mixing until melted.
Remove saucepan from heat, and mix in cooked pasta, mushrooms, peppers, spinach, and soy sauce. Mix until incorporated.
Transfer to the prepared baking dish, and top with the ¼ cup of parmesean.
Bake 20 minutes, until bubbly and light brown.