Preheat the oven to 350 degrees F. Grease a 9-by-14-by-2-inch oval baking dish, or six individual cast-iron pans, with 2 tablespoons of the melted butter and set aside.
Heat 2 tablespoons olive oil in a large (12-inch) saute pan over medium-high heat. Add the scallions and zucchini and saute for 2 minutes. Add the garlic and cook for one minute. Lightly press most of the water out of the spinach and add it to the pan. Add the rice, basil, parsley, nutmeg, lemon juice, 2 teaspoons salt, and 1 teaspoon pepper and toss well. Transfer to the prepared baking dish.
In a medium bowl, whisk together the eggs, cream, the -remaining 2 tablespoons melted butter, and the 1/4 cup Parmesan. Pour the mixture over the spinach and zucchini and smooth the top. Sprinkle with some extra Parmesan and the Gruyere. Bake for 20 to 30 minutes, until a knife inserted in the center comes out clean.