Bring a pot of water to a boil. Cook broccoli for 3 minutes; drain. Rinse in cold water; drain.
Preheat oven to 350ºF. Line a 9-by-13-inch baking dish with foil, leaving a 2-inch overhang on each short side. Mist with cooking spray.
Warm oil in a skillet over medium heat. Add onion, mushrooms, zucchini, squash and bell pepper. Add 1 tsp. salt and 1/2 tsp. pepper. Sauté for 7 minutes. Add spinach, peas, corn and broccoli; sauté for 3 minutes. Season with salt and pepper. (Mixture can be made up to 1 day ahead. Cover; chill.)
Whisk eggs, sour cream, chives and Parmesan. Stir in vegetables. Pour into dish; bake until a toothpick inserted in center comes out clean, about 30 minutes. Let rest on a rack for 20 minutes. Using foil, move frittata to a cutting board. Peel off foil; cut frittata. Serve warm or at room temperature.