Cook pasta according to package directions. Drain and keep warm.
Meanwhile, melt butter in a large fry pan over medium high heat. Add zucchini, carrots, mushrooms, garlic and thyme. Cook, stirring often, until tender. Stir in flour. Add the milk all at once. Cook and stir until thickened and bubbly.
Remove pan from heat. Add cheese, stirring until just melted. Add cooked pasta to vegetable sauce mixture and mix lightly.
Season with salt and pepper to taste. Offer Parmesan Cheese.