Preheat oven to 375 degrees. Heat a nonstick ovenproof 10-inch skillet sprayed with olive-oil or vegetable-oil cooking spray over medium heat. Add mushrooms, season with salt and pepper, and cook over medium heat until wilted, about 5 minutes.
In a large bowl, whisk egg whites until they form soft peaks. In another large bowl, whisk whole eggs until foamy and lemon-colored. Fold the egg whites into the eggs.
Sprinkle mushrooms with chopped sage. Pour egg mixture into pan with mushrooms. Distribute whole sage leaves evenly over eggs. Cook until edges are set, about 5 minutes. Transfer to oven, and cook until set and golden brown, about 7 minutes. Drizzle greens with red-wine vinegar and extra-virgin olive oil. Season with salt and pepper. Cut frittata into wedges, and serve over greens.