Preheat oven to 375°F (190°C). Slice zucchini lengthwise, scoop out centers leaving a ¼-inch border, brush with olive oil, and season with salt and pepper.
Place zucchini cut-side up on a baking sheet and bake for 10 minutes, then remove and set aside.
Heat a skillet over medium heat, add olive oil, cook mushrooms until moisture evaporates, then add garlic and spinach and cook until wilted. Remove from heat and let cool slightly.
In a bowl, mix ricotta, egg, Parmesan, salt, pepper, and nutmeg until smooth. Stir in the cooled spinach-mushroom mixture.
Spoon filling evenly into zucchini halves and sprinkle with mozzarella. Drizzle lightly with olive oil or butter.
Bake uncovered for 25–30 minutes until cheese is melted and lightly golden and zucchini is tender.
Optional: broil for 2–3 minutes at the end for a more golden top. Let rest 5 minutes before serving.