Whisk together eggs, basil, parsley, salt, and pepper in a bowl.
Cook prosciutto in oil in a 12-inch ovenproof nonstick skillet over moderate heat, stirring, until edges begin to crisp, about 2 minutes. Add zucchini and chard and cook, covered, stirring occasionally, until vegetables are just tender, about 8 minutes. Add scallions and zucchini blossoms and cook, uncovered, stirring occasionally, until just wilted, 1 to 2 minutes. Pour egg mixture into skillet and cook, lifting up cooked egg around edge using a spatula to let as much raw egg as possible flow underneath, until edge is set, about 2 minutes (top and center will still be very loose). Sprinkle cheese evenly over top.
Broil frittata about 6 inches from heat until set, slightly puffed, and golden, 2 to 2 1/2 minutes.
Cool frittata 5 minutes, then loosen edge with a clean spatula and slide onto a large plate. Cut into wedges.
*Available at many farmers markets and specialty produce markets.