Preheat the oven to 350ºF. Line a muffin pan with muffin cups.
Spread the bran on a cookie sheet and bake for 6 to 8 minutes, until toasted, stirring half-way through to prevent the bran from burning.
In a small saucepan, stir together 1 cup of the chopped dates and 1 cup of water. Simmer on low heat for about 15 minutes until the water is absorbed.
Place the mixture in a blender and process until pureed.
Pour the bran into a large bowl, add the buttermilk and remaining 1/2 cup water. Stir to combine.
Stir in the date puree, orange zest and brown sugar.
Add the olive oil along with one whole egg and one egg white (discard the remaining yolk) and mix well to incorporate.
Stir in the all-purpose flour, whole wheat flour, baking powder, baking soda and salt.
Stir in the remaining chopped dates.
Spoon the mixture into the muffin cups and bake until the muffins are firm to the touch, about 25 minutes. Remove and let cool slightly then serve.