For cookies, whisk together first 4 ingredients in a medium bowl.
Beat butter and sugars together in a separate medium bowl until light and fluffy. Scrape down sides and bottom of bowl, and add the egg white and the extracts; beat until just combined.
Add flour mixture, and stir until incorporated. Cover bowl with plastic wrap, and chill for at least 4 hours.
Preheat oven to 325 degrees F. Line 2 baking sheets with parchment paper.
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 sheet. 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 mnutes. Transfer the cookies to a wire rack to cool completely.
For the icing, whisk together all the icing ingredients in a large bowl until completely smooth. Mixture should have the consistency of a glaze. If it's too thin, add a bit more sugar. If it's too thick, add a few more drops of lemon juice.
Transfer icing to a pastry bag (or a zip-top plastic bag with a small hole in one of the bottom corners). First, outline the cookie or desired design, then fill it inches Let icing harden before serving. Cookies can be kept in an airtight container for up to 3 days.