Preheat the oven to 375°F.
Coat a large oven-safe skillet with oil spray and preheat over medium-high heat.
Add the bell pepper, onion and chard and sauté until the vegetables are soft, about 5 minutes. Add the garlic and sauté for 1 minute.
Meanwhile, in a large bowl, whisk together the whole eggs, egg whites, and black pepper to taste. Pour the egg mixture over the sautéed vegetables and cook, without stirring, for 2 minutes. Sprinkle the feta over the egg mixture.
Place the pan in the oven and cook for 10 minutes, or until the eggs are set and puffed.
Allow the frittata to cool in the pan for about 5 minutes. With a spatula, turn the frittata out onto a cutting board, cut it into quarters, and serve.