Baked Spinach and Zucchini

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4 tablespoons (1/2 stick) unsalted butter, melted, divided

Good olive oil 

6 scallions, white and green parts, sliced 1/4 inch across 

1 pound small zucchini, sliced in 1/4-inch-thick rounds (4 zucchini) 

1 tablespoon minced garlic (3 cloves) 

2 (10-ounce) packages frozen chopped spinach, defrosted 

1 cup cooked basmati rice 

1/4 cup chopped fresh basil leaves 

1/4 cup chopped fresh parsley 

1/2 teaspoon ground nutmeg 

2 tablespoons freshly squeezed lemon juice 

Kosher salt and freshly ground black pepper 

4 extra-large eggs 

3/4 cup heavy cream 

1/4 cup freshly grated Italian Parmesan cheese, plus extra 

2 ounces Gruyere cheese, grated