Line 2 baking sheets with parchment paper and set aside.
Whisk together flours, salt, and baking soda in a medium bowl.
Beat butter and sugars together in a separate medium bowl with an electric mixer until light and fluffy. Scrape down sides and bottom of bowl. add egg white and extracts; beat until just combined. add flour mixture; stir until incorporated. Cover bowl with plastic wrap, and chill for at least 4 hours.
Dust a work surface with flour. Turn out chilled dough directly onto work surface.
Roll dough out to a 1/4-inch thickness. Use cookie cutters to cut shapes in dough, and gently transfer them to baking sheets. (You can reroll the scraps, just be sure to chill in between.)
Bake cookies for 12 minutes or until set but not browned.
Remove cookies from oven, and cool for 5 minutes.
Transfer cookies to a wire rack to cool completely.
Whisk together sugar, egg whites, and lemon juice in a large bowl until completely smooth. (If the icing is too thin, add a bit more sugar. If its too thick, add a few more drops of lemon juice.)
Transfer icing to a pastry bag (or a resealable plastic bag with a small hole cut into one of the bottom corners). First, outline the cookie with icing, then fill it in, if desired.
Let icing harden before serving. Cookies can be kept in an airtight container for up to 3 days.
