Preheat oven to 425°F (220°C); set aside a lightly greased or parchment paper lined baking sheet.
In a large bowl, whisk together flour, bran, brown sugar, baking powder, baking soda and salt. Using a cheese grater, grate the butter into the dry ingredients; toss to mix so butter is evenly coated. In a small bowl, whisk together the buttermilk and egg and add all but 2 tsp (10 mL) of liquid to dry ingredients; stir until mixture just comes together.
Gather the dough into a ball. On a lightly floured surface, pat dough into a rectangle, about 1/2 inch (1 cm) thick. Fold it into thirds over itself, then pat the dough into a rectangle, about 1 inch (2.5 cm) thick and cut into 8 squares.
Transfer to prepared baking sheet and brush tops with remaining buttermilk mixture; sprinkle with coarse sugar. Bake 15 to 20 minutes, until golden brown. Transfer to a wire rack to cool.