Preheat the oven to 400°F and spray the muffin tins with cooking spray or line them with paper liners.
In a medium bowl, sift together 1 cup all-purpose flour, 2 tsp baking powder, 1 tsp salt, and ½ tsp baking soda.
Add in 2 cups wheat bran and mix together.
In a separate large bowl, cream together ⅓ cup softened unsalted butter and ½ cup granulated sugar using a hand mixer. Add in 1 egg and mix until fully combined.
Mix half of the dry ingredients into the wet mixture until just combined. Then add in 1 cup buttermilk and mix again.
Repeat with the remaining dry ingredients and the final cup of buttermilk, mixing only until everything is just combined.
Divide the batter into the muffin tins and bake in the preheated oven for 20 minutes. Once done, let them cool for 10 minutes, then transfer to a wire rack to cool completely.