Whisk all the eggs, 1½ tablespoons cheese, ¼ teaspoon salt, and ¼ teaspoon pepper in large bowl.
Heat olive oil in medium nonstick broiler-proof skillet over medium heat. Add onion and sauté until tender but not brown, about 6 minutes.
Add Kale/ Red chard in 3 batches; toss until each begins to wilt before adding next. Sprinkle with salt and pepper.
Sauté until any liquid in skillet evaporates. Increase heat to medium-high; add salami and garlic to skillet and stir 1 minute. Add eggs to skillet; stir to distribute evenly. Reduce heat to medium-low, cover, and cook until eggs are almost set but still moist in center, about 4 minutes. Sprinkle remaining 1½ tablespoons cheese over top.
Transfer frittata to broiler and cook just until set in center and beginning to brown, about 1 minute.
Using flexible spatula, loosen frittata around edges. Slide frittata out onto platter. Serve warm or at room temperature.