Beat eggs, water, and salt in a small bowl.
Preheat broiler. In a 6-inch ovenproof skillet, melt half the butter over medium-high heat. Pour in half the egg mixture; add half of the vegetables and basil. Cook, lifting edges of frittata with a spatula to drain liquid from center. When the mixture is almost cooked, sprinkle with half the cheese and place under broiler. Broil until the top is light golden brown, about 2 to 3 minutes. Sprinkle with pepper. Repeat with remaining butter, egg, vegetables and basil, and cheese. Serve hot.