Arrange the oven shelf in the bottom 1/3 position in the oven. Preheat oven to 375ºF (190ºC). Spray a 9-inch pie plate with nonstick cooking spray; set aside. 
In a 12-inch nonstick skillet, heat the oil (2 tablespoons) over medium-high heat. Stir in mushrooms (8 ounces) and sauté, stirring constantly, until soft, about 8 minutes,
 Stir in onion (1 1/2 cups) and garlic (1 tablespoon) and continue to sauté, stirring frequently, until tender, about 7 minutes.
 Stir in spinach (5 ounces), then continue to sauté, tossing the spinach with tongs, until wilted. Remove from heat. Cool slightly.
 In a large mixing bowl, add eggs (6), heavy cream (1/2 cup), mustard (1 tablespoon), thyme (1 tablespoon), salt (3/4 teaspoon), and pepper (1/8 teaspoon), and whisk until well combined.
 Gently fold in the cooled mushroom mixture and cheese (1 1/2 cups).
 Pour into prepared pie plate. Place pie plate on a large rimmed baking sheet and place in preheated oven. Bake until custard is set and top is beginning to brown, about 30 minutes. Let quiche sit 10-12 minutes before slicing. Garnish with extra fresh thyme. Serve.