Preheat broiler. Whisk eggs, basil, parsley, salt and pepper in bowl.
Heat 1 tablespoon olive oil over medium heat in each of two (12-inch) oven-proof nonstick pans.
Stir into each pan half the garlic, yellow squash, zucchini, red peppers and mushrooms.
Cook, stirring occasionally, until vegetables are tender, about 8 minutes. Add green onions; cook 3 minutes.
Pour half of the egg mixture into each pan. Cook eggs until set, about 3 to 4 minutes.
Sprinkle half of the goat cheese over each frittata. Broil 5 to 7 inches from heat until slightly puffed, golden, firm throughout, and thoroughly cooked, about 3 minutes.
Allow frittata to set 5 minutes before cutting each into 6 wedges. Serve immediately.