Boil a large pot of water and cook the penne for 7 minutes or until al dente. Drain and return the pasta to the pot.
In a large skillet, heat the olive oil and sauté the mushrooms for 4 minutes or until tender. Add the spinach to the skillet and sauté until reduced in size and wilted about 2 minutes. Place vegetables in the same pot as the pasta. Set aside.
To make the Alfredo sauce, heat the olive oil in the same skillet used for the vegetables. Add the garlic and sauté for one minute. Add the flour to the skillet and cook for an additional minute. Slowly whisk in the chicken broth and milk. Bring the mixture to a simmer and cook until thickened, about 3 minutes. Stir Parmesan cheese and salt into the sauce. Pour the sauce into the pot with the pasta and vegetables. Add the chicken to the mixture and gently toss until everything is evenly coated.
Place half of the chicken/noodle mixture in a 9x13-inch pan coated with non-stick cooking spray. Sprinkle half of the mozzarella cheese on top. Layer the remaining pasta over the cheese and sprinkle the rest of the cheese evenly over the top.
Bake in a 350°F oven for 15 to 20 minutes or until light, golden brown and bubbly. Remove from the oven and serve immediately. Leftovers can be kept in an airtight container in the refrigerator for up to 3 days.
Notes: Other sautéed vegetables, like broccoli or peas, can be substituted for the mushrooms and spinach.