Measure out the 3 cups of bran flakes and then finely crush them by hand or in a food processor. In a large bowl, mix the crushed bran flakes in with the flour and brown sugar, cinnamon, baking powder and salt.
In a separate bowl, mix the oil, buttermilk, egg and vanilla extract. Mix the wet ingredients in with the dry ingredients. Fold the blueberries into the batter mixture. Mix until thoroughly combined. For best results, refrigerate the batter for a few hours prior to serving to allow the bran cereal to break down.
Line a muffin tin with muffin paper liners. Add a few spoonfuls of the batter into each muffin liner until it is at least 3/4 full. Sprinkle with cane sugar.
Bake in preheated oven for 18-20 minutes. Remove from oven, cool and serve.