Preheat oven to 375°F.In a small bowl stir together 2 tablespoons granulated sugar and cinnamon. Into a large bowl sift together flour, remaining tablespoon granulated sugar, baking powder, and salt.
Cut butter into small pieces and with your fingertips or a pastry blender blend into flour mixture until mixture resembles coarse meal. In another small bowl whisk together egg and 3 tablespoons milk and add to flour mixture, stirring until just combined.
Transfer mixture to a lightly floured surface and gently knead, 3 or 4 times, until it forms a dough. Pat dough into a 10- by 6-inch rectangle (about ‚ inch thick).
Brush dough with some remaining milk and sprinkle evenly with cinnamon sugar. Beginning with a short side, roll up rectangle to form a 6-inch log and cut crosswise into 4 pieces. Arrange pieces on a baking sheet, cut sides up, with seams touching.
Bake buns in middle of oven until pale golden and cooked through, about 18 minutes.
In another small bowl stir together confectioners' sugar and water until smooth and drizzle over warm buns.
