Prepare Swiss chard: Clean and check leaves thoroughly. Cut off long stems from Swiss chard leaves. Chop stems and set aside. Chop leaves into 1-2 inch strips and set aside.
Beat eggs in a large bowl until well blended. Season to taste with salt and pepper; set aside.
Heat oil in a large frying pan (oven-safe) over medium high heat until oil is hot. Add reserved stems, onion, and garlic. Season with salt and freshly ground black pepper to taste. Sauté for about 5-7 minutes until onions are translucent and soft.
Add beaten eggs. Use spatula to stir and gently form large curds. Allow eggs to set for about 2 minutes. Add reserved chard leaves and chopped tomato; distribute evenly amongst eggs. Sprinkle evenly with parmesan cheese.
Transfer pan to broiler. Finish cooking under broiler for another 3-5 minutes, or until eggs are cooked and cheese is nicely browned.
Remove from broiler. Cut into wedges and serve warm.