Preheat your oven to 325 degrees and spray a 12-cup muffin tin with cooking spray. (I use my olive oil mister)
In a bowl combine the wheat bran and the buttermilk, stir and set off to the side while you prep the rest of the ingredients.
In another bowl, combine the whole wheat flour, baking powder, baking soda and salt. Stir to combine.
To the bowl with the wheat bran, add the applesauce, egg, honey, brown sugar and vanilla. Stir to combine before pouring into the bowl with the flour. Stir until just combined and scoot off to the side.
Gently toss the berries with a tablespoon of all purpose flour until coated, then add them to the bowl with the muffin batter. Gently fold the berries into the batter.
Divide the bran muffin batter into the prepared muffin tin. Sprinkle with turbinado sugar (if using) and slide the pan onto the middle rack of your preheated oven.
Bake for 22 to 24 minutes, or until a toothpick comes out clean with only a few crumbs attached. Rotate the pan halfway through to ensure even baking.
Allow the muffins to cool in the pan for 20 minutes before running a knife or offset spatula around the edges and removing. Transfer the muffins to a wire rack.
These muffins will last for a few days on the counter.