Step 1: Sauté vegetables. Preheat the oven to broil. Use a well-seasoned, 10-inch iron skillet or a nonstick skillet with a heatproof handle. Heat 1 tablespoon olive oil in the skillet over medium-high heat, and add 1 cup minced onion. Cook until the onion is translucent, about 3 minutes.
Step 2: Add the egg mixture to pan. Whisk together 4 large eggs and 2 egg whites, and season with 1/4 teaspoon pepper. Pour the egg mixture over the onions, patting down any lumps with a wooden spoon. Scatter 3 ounces sun-dried tomatoes, packed without oil evenly over the pan surface.
Step 3: Add cheese and put in broiler. Distribute 1/4 cup (2 ounces) goat cheese over the top of the frittata, then place the skillet under the broiler for 2 minutes, until the frittata rises slightly and becomes light and settled. Remove from broiler and top with 1/4 cup basil chiffonade. (Stack basil, then roll the stack, and slice it into feathery, 1/4-inch pieces.)
Step 4: Plate and serve. To remove the frittata from the iron skillet, place a large plate over the top of the pan, invert the frittata onto the plate, and cut it into wedges. With a nonstick skillet, slide the frittata onto a serving plate, then cut into wedges.