Preheat oven to 350 degrees. In a 10-inch oven-proof nonstick skillet heat 2 teaspoons oil over medium heat. Add leeks and season with salt and pepper. Cover, and cook, stirring occasionally, until soft, 4 to 6 minutes. Stir in tomatoes, cover, and cook 2 minutes more. Transfer to a bowl.
In a large bowl, beat egg whites with salt and pepper to stiff peaks; add egg yolks and whisk to combine.
Brush skillet with remaining 1 teaspoon oil. Add eggs, tilting skillet to evenly distribute. Sprinkle with vegetables and goat cheese, pushing gently under surface. Cook over medium heat until sides are dry, 3 to 4 minutes. Transfer to oven and bake until puffed and golden, 15 to 20 minutes.