Beat the butter and sugars together until light and fluffy. Add in the egg, vanilla and zest and beat to combine.
Add the flour, salt and cinnamon and mix until incorporated. Wrap the dough in plastic wrap and refrigerate at least 1 hour.
Roll the dough out on a well-floured surface to about 1/4" thick. Cut out shapes with cookie cutters or cut in to squares with a pastry wheel/pizza cutter. Place the cookies on a parchment paper-lined cookie sheet.
Beat the egg and milk together with a fork or whisk. Mix together the sugar and cinnamon. Use a pastry brush to coat the cookies in the egg mixture, then sprinkle the cinnamon sugar on top.