Place the oven rack in the upper third position then preheat the oven to 425 degree F. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder and salt. Add the butter and using a fork or pastry blender, cut into the flour mixture until the butter pieces are the size of small peas.
In a large bowl, combine the mashed banana, milk and vanilla. Add the dry ingredients and mix until just moistened.
Transfer the dough onto a lightly floured surface. Roll into a 12-inch square.
In a small bowl, combine the brown sugar and cinnamon. Sprinkle over the entire surface of the dough.
Tightly roll the dough into a log. Flatten the log until it is 1 inch thick and 16 inches long. Cut into 6 rectangles, then halve the rectangle into 2 triangles. Place on the prepared baking sheet, leaving space in between.
Brush the scones with milk and then bake for 15 to 18 minutes or until golden brown.