How to Make It
Using a vegetable peeler, shave zucchini into long, even strips. Toss with 1/4 teaspoon salt in a colander. Let stand until ready to use.
Heat oil in a Dutch oven over medium-high. Add onion and garlic; cook, stirring often, until tender, about 3 minutes. Add mushrooms; cook, stirring often, until browned, about 5 minutes. Add tomato paste; cook 1 minute. Stir in tomatoes, pepper, and remaining 1/2 teaspoon salt; bring to a simmer, stirring often. Reduce heat to medium low, and simmer, stirring occasionally, until slightly reduced, about 6 minutes. Stir in spinach; cover and cook until spinach wilts, about 3 minutes. Remove from heat. Gently stir in zucchini strips.
Stir together ricotta and mozzarella in a microwavable bowl; microwave at high 30 seconds. Dot zucchini mixture with cheese mixture. Sprinkle with basil.