Preheat oven to 400 degrees F.
Heat olive oil and butter in a large oven safe frying pan on medium heat
Add anchovies and stir until dissolved (about 1 minute).
Add sliced zucchini, sliced mushrooms, salt, pepper and dried basil. Sauté until zucchini starts to brown and mushrooms are soft (5-10 minutes.)
Remove zucchini and mushrooms from pan.
Add ½ cup tomato sauce to bottom of pan.
Layer ½ of zucchini/mushroom mixture on top of the tomato sauce.
Layer ½ of sliced mozzarella on top of zucchini/mushroom mixture.
Layer 1/2 cup of tomato sauce on top of cheese.
Layer rest of zucchini/mushroom mixture and then 1/2 cup more of tomato sauce and then top with rest of mozzarella.
Sprinkle grated parmesan on top.
Bake in oven for 20 minutes.