You can omit the cooked egg whites, and this dish still will taste delicious. If you prefer small-grain kasha, increase the water to 1/2 cup.
Place kasha in a medium saucepan; cook over medium-low heat 3 minutes, stirring often. Gradually add uncooked egg whites, stirring to coat. Add 1/4 cup water, salt, and broth; bring to a boil. Cover, reduce heat, and simmer 15 minutes or until liquid is absorbed. Remove from heat. Cut cooked eggs in half; remove yolks, and reserve for another use. Finely chop cooked egg whites. Add cooked egg whites and 1 1/2 teaspoons oil to kasha mixture; stir well.
Heat 1 1/2 teaspoons oil in a medium nonstick skillet over medium-high heat. Add leek; sauté 5 minutes. Add 2 tablespoons water and sugar; cover, reduce heat, and cook 2 minutes. Spoon 1 cup kasha into each of 4 bowls. Top each serving with 1/2 cup leek mixture and 1 tablespoon chopped pecans.