Combine the all-purpose and whole wheat flours, the bran, baking powder, soda, salt, cinnamon and brown sugar. Cut in the butter. (Or combine in a food processor, just until crumbly.) Add the egg, buttermilk, and dates; do not overmix. (If the dough seems too sticky to work with add a couple more tablespoons flour.) Shape the dough into a rectangle about 1 inch thick on a floured surface. Cut into 12 triangles.
Bake on an ungreased baking sheet in a preheated 350 degree F oven about 25 minutes. Cool on a rack.