Position a rack in the upper third of the oven and preheat to 350 degrees F. Cut the chard stems crosswise into slices 1/4 inch thick. Coarsely chop the leaves.
In large frying pan over medium heat, warm 2 Tbsp of the olive oil. Add onion and saute until tender, about 6 minutes. Add chard stems, season with salt and saute about 4 minutes. Add chopped leaves and saute until tender, 2 to 3 minutes. Transfer to plate. Set aside.
In large bowl, lightly beat the eggs with garlic and cheese. Season with cayenne, salt and black pepper.
Gently squeeze liquid from chard and stir in egg mixture. In an 8-inch ovenproof frying pan over medium-high heat, warm remaining 2 Tbsp olive oil. Add egg mixture, reduce heat to medium and cook until the eggs are set around the edges, about 5 minutes. Transfer to the oven and cook until set, 7 to 9 minutes longer. Let cool briefly.If desired, invert frittata onto large plate.
Cut into wedges and serve right away. Serves 4 to 6.