In a medium bowl, mix together wheat bran and buttermilk and let stand for 10 minutes.
In another bowl, beat together oil, egg, sugar, and vanilla. Add to the bran and buttermilk mixture and stir until combined.
In a third bowl, sift together the flour, baking soda, baking powder, salt, and cinnamon. Stir this into the wet mixture and mix until just blended.
Pour batter into prepared muffin tins to about ¾ full and bake for 16-18 minutes or until a toothpick in the center comes out clean.