Preheat oven to 450 degree F. For pastry, in a medium bowl stir together flour, 2 teaspoons of the fresh thyme or 3/4 teaspoon of the dried thyme, and 1/4 teaspoon of the salt; cut in 1/2 cup of the butter until pieces are pea-size. Add cold water, 1 tablespoon at at time, until dough forms, tossing with a fork to moisten evenly. Form dough into a ball. On a lightly floured surface, roll dough to a circle about 12 inches in diameter. Carefully transfer to a 9-inch pie plate; ease into plate. Trim pastry to 1/2 inch beyond edge of pie plate. Fold under extra pastry and flute as desired. Prick bottom and sides with a fork. Line pastry with a double thickness of foil. Bake 8 minutes. Remove foil. Bake 5 to 6 minutes more or until golden. Cool on wire rack. Reduce oven temperature to 325 degree F.
Meanwhile, in a large skillet heat 1 tablespoon of the remaining butter over medium heat. Add mushrooms and garlic. Cook, stirring frequently, until mushrooms are tender, about 4 minutes. Add spinach and green onion; cover and cook until spinach is wilted, about 2 minutes. Transfer mixture to a colander to drain excess liquid.
In a large bowl combine eggs, half-and-half, remaining 1 teaspoon fresh thyme or 1/4 teaspoon of the dried thyme, the remaining 1/4 teaspoon salt, nutmeg, and pepper. Melt the remaining butter over medium heat in the same skillet. Add egg mixture to skillet. Cook, without stirring, until mixture begins to set on the bottom and around edges. With a spatula or large spoon, lift and fold the partially cooked egg mixture so the uncooked portion flows underneath. Continue cooking over medium heat for 2 to 3 minutes or until egg mixture is cooked through but still glossy and moist. Remove from heat; fold in mushroom mixture and Gruyere cheese. Spoon into baked pastry shell.
Sprinkle Parmesan cheese atop egg mixture. Bake, uncovered, for 12 to 15 minutes or until filling is heated through and cheese is melted. Makes 6 servings.