Wash the Swiss chard, remove and discard the large stems, and finely chop the leaves.
In a 10- to 12-inch nonstick skillet, saute the garlic and onions in 1 teaspoon of oil for 3 minutes on medium heat. Add the Swiss chard, stir, cover, lower the heat, and cook for about 10 minutes. Remove the skillet from the heat and drain the Swiss chard.
In a mixing bowl, beat the egg whites, eggs, basil, salt, and pepper until blended. Stir in the sauteed Swiss chard.
Coat the bottom of the skillet with the remaining teaspoon of oil and return to medium heat. When the skillet is hot, pour in the Swiss chard-egg mixture and arrange the tomato slices on top. Cover and cook for 5 to 8 minutes, until the edges are firm and the bottom is golden and beginning to brown.
Place a large, flat plate or pizza pan over the skillet and flip the skillet over so that the frittata falls onto the plate. Slide the frittata back into the skillet and cook for another 5 minutes, or until the eggs are fully cooked.
Serve immediately or at room temperature, topped with grated Parmesan if desired.