Preheat oven at 425F. Cover 2 large cookie sheets with parchment paper, Silpat, or lightly butter them.
In a large bowl sift together the flour, baking soda, a pinch of salt, and ½ cup sugar. Cut the butter into bits and blend it into the flour mixture with your fingertips until the mixture resembles a coarse meal.
In a small bowl, mix together 2 eggs and the milk until well combined. Add milk mixture and bananas to the flour mixture, gently stirring into the dough just forms.
On a lightly floured surface form dough into a ball and flatten it into a disk. With a floured rolling pin, roll out dough 1 inch thick and with a 3-inch round cutter cut out rounds, transferring to baking sheets.
If the dough sticks, dip the cutter into flour before cutting the rounds. Gather scraps and make more rounds in the same manner.
In a small bowl, beat 1 egg and brush tops rounds, and sprinkle the remaining 2 tablespoons of ugar over them.
Bake scones in the upper and lower thirds of the oven, switching them halfway through baking, 20 minutes, or until golden. Transfer scones to a rack and cool.