1. Heat oven to 400 degrees. Coat a 12-inch nonstick ovenproof skillet with olive oil cooking spray, and place over medium-high heat. Add mushrooms and onion, and saute until mushrooms start to release their juices, stirring frequently. Reduce heat to medium low, and cook until mushrooms are soft and golden brown. Add Swiss chard, thyme, 1/4 teaspoon salt, and pepper, and cook until wilted and all the liquid has evaporated. Transfer to a baking pan lined with paper towels, and set aside.

2. Combine eggs, egg whites, and remaining 3/4 teaspoon salt in the bowl of an electric mixer fitted with the whisk attachment, and whip until soft peaks form, 4 to 5 minutes. Coat a clean 12-inch nonstick ovenproof skillet with olive-oil cooking spray, and place over medium-high heat. Add two-thirds of the egg mixture to the pan, layer with reserved vegetables, and top with remaining egg mixture. Sprinkle top with Parmesan, and transfer pan to oven. Cook until eggs are set and frittata is golden brown, about 15 minutes. Run a spatula around edges of pan to loosen frittata if necessary; transfer to a serving plate. Cut into wedges, garnish with thyme sprigs, and serve.