Heat oven to 375 degrees F.
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. Add egg mixture to 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.
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