In a medium-sized mixing bowl mix together the sugar, butter and vanilla on medium speed about 3 minutes until light and fluffy. Add flour and stir until the dough comes together. Flatten into a disk, wrap with plastic wrap and refrigerate about 1 hour.
Lightly flour a piece of waxed paper and roll the dough into a rectangle.
In a small bowl whisk the egg white and water together until foamy. In a separate small bowl whisk the sugar and cinnamon together. Brush the egg white all over the dough and sprinkle the cinnamon sugar evenly over top.
Starting with a long edge roll the dough carefully into a log sealing the edge with the egg white. Wrap in plastic or waxed paper and freeze until firm.
Set oven to 350. Use a sharp knife to cut the log into 1/2-inch slices. Bake for 12 minutes, remove to wire rack to cool.
Sift powdered sugar into a bowl and whisk in the milk and vanilla until smooth. Drizzle over the cooled cookies.
*Tweaked recipe from