Preheat oven to 425 degrees. Combine in a large bowl, diced peeled eggplant, chopped onion, diced mushrooms, diced zucchini, diced red pepper, salt and pepper. Toss together with olive oil.
Bake at 425 degree F. on baking sheet for 45 minutes stirring every 15 minutes or till soft. Spoon back in bowl.
Mix in crumbled feta cheese or chèvre, and chopped fresh basil. Roll out bread dough to a thickness of about 1/4 inch. Cut into 7-inch circles. Spoon 1/2 cup of the vegetable mixture over circles.
Brush edges of dough with egg white. Fold dough into turnovers. Seal and brush with egg white.
Bake till golden. Mixture can also be used for pizza or for pasta.