In a skillet heat 1 tablespoon of the olive oil over medium heat. Cook and stir onion in hot oil for 5 minutes or until golden brown. Set aside.
Preheat oven to 375 degree F. In a large mixing bowl combine all-purpose flour, whole wheat flour, cheese, basil, baking powder, baking soda, and salt. Make a well in the center of dry ingredients. Slightly beat one of the eggs. In a small mixing bowl stir together remaining oil, buttermilk, and the beaten egg. Stir in onion mixture. Add buttermilk mixture to flour mixture, stirring until flour mixture is just moistened.
With floured hands, knead gently in bowl 2 to 3 times or until dough is nearly smooth. Shape into two 4-inch rounds. (Or, shape into one 6-inch round loaf.) Place on a lightly greased or parchment-lined baking sheet.
Slightly beat the remaining egg with 1 tablespoon water. Brush loaf with egg mixture. Arrange tomato slices on top. Bake for 25 to 30 minutes or until golden. Cool slightly on a wire rack; serve warm or at room temperature. Keep for 2 or 3 days at room temperature in a paper bag. Makes 12 servings.