Heat 1 1/2 teaspoons oil in a large cast-iron skillet over medium-high. Add half of the zucchini; cook 3 minutes on each side or until browned. Remove from pan. Repeat procedure with 1 1/2 teaspoons oil and remaining zucchini. Add remaining 1 tablespoon oil to pan. Add onion and mushrooms; saute for 6 minutes. Stir in spinach and garlic; cook for about 1-2 minutes. Remove pan from heat.
Spread mushroom mixture in bottom of pan; top with cooked zucchini. Pour 2 cups tomatoes over zucchini; season with salt. Arrange noodles over top. Spread remaining tomatoes over the noodles; top with ricotta. Cover, and simmer 20 minutes over medium-low or until noodles are done.
Remove pan from heat. Preheat broiler with oven rack in top position.
Sprinkle mozzarella over the top; broil 3 minutes or until melted and lightly browned.