1 1/2 cups water
1/2 cup white sugar
1 tablespoon distilled white vinegar
1 1/2 tablespoons vegetable oil
3 tablespoons all-purpose flour
1/2 teaspoon baking powder
1/4 teaspoon salt
1 cup whole wheat flour
1 egg, beaten
1 teaspoon white sugar
1/2 teaspoon vanilla extract
Mix water, sugar, vinegar, oil and flour in a large saucepan. Bring to a boil, stirring constantly. Boil until thickened, about 20 minutes. Remove from heat; stir in flour, baking powder and salt. Allow to cool.
While the mixture is simmering, mix egg and 1/2 teaspoon sugar with the vinegar mixture. Heat slowly, whisking constantly until the egg is cooked. Strain egg mixture over the water and sugar mixture to bring just to a boil.
Stir the whole wheat flour into the water and vinegar mixture. Turn over gently, and whisk in the flour mixture until just blended. Gradually whisk in the remaining flour, beating frequently until the flour is incorporated. Pour the mixture into the baking dish.
Bake in the preheated oven for 40 minutes, or until a toothpick inserted into the center of the dish comes out clean. Cool completely before storing in an airtight container.
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