In a medium bowl, whisk together the flour, salt, and baking powder and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter, shortening, and sugar together until light and fluffy. Add the egg and vanilla and beat until just combined. Add the flour mixture and mix until incorporated. Wrap the dough in plastic and refrigerate for at least 4 hours.
Dust a work surface with a sprinkling of flour. Unwrap the chilled dough, and put it directly on the work surface. Roll the dough
In a large bowl, whisk together the sugar, egg whites, and lemon juice until the mixture is completely smooth. The mixture should have the texture of a glaze. If the mixture is too thin, add a bit more sugar. If the mixture is too thick, add
The best way to ice sugar cookies is with a pastry bag fitted with a small or medium tip. First, outline the cookie or design, then fill it in. Let the icing harden before serving.
The cookies can be kept in an airtight container for up to 3 days.