With the rack in the middle position, preheat the oven to 350 degrees. Whisk the eggs, salt, and pepper together in a medium bowl. Stir in the vegetables and basil.
Heat a 12-inch ovenproof nonstick skillet over medium heat; once hot, add the oil. Add the egg mixture and cook, without stirring, for 1 minute. Transfer to the oven and bake until the eggs are set and the top is golden, 15- 20 minutes. Turn the frittata out onto a serving plate, cut into wedges, and serve.