Make the cookies: In a medium bowl, combine the flour, salt, baking soda and baking powder. Set aside.
In the bowl of a stand mixer, cream the butter and sugar on medium-high speed until pale and fluffy, 4 minutes. Add the egg and mix until combined. Stir in the vanilla and almond extracts.
Reduce the mixer speed to low and add the flour mixture until just combined. Wrap the dough tightly in plastic wrap, using the plastic to help shape the dough into a disk. Refrigerate for a minimum of 30 minutes, up to 2 days, or freeze for up to 1 month.
While the cookies are chilling, make the icing: In a large bowl, whisk the powdered sugar with the egg whites, lemon juice and 1 teaspoon of water, adding more water as needed, until a thin and shiny glaze forms. Cover with plastic wrap, letting the wrap touch the icing, until ready to use. Makes about 2 cups.
Preheat the oven to 350°. Line a cookie sheet with parchment paper and set aside.
Lightly flour a kitchen surface, place the dough disk on top and lightly flour the dough. Using a rolling pin, gently pound the dough to a ½-inch thickness, then roll to a generous ⅛-inch thickness. Use a cookie cutter to punch out shapes and transfer them to the prepared baking sheet. Gather the scraps into a bowl and roll them out up to 2 times more, chilling if the dough becomes too sticky. Bake until the bottoms and edges of the cookies begin to turn golden brown, 7 to 10 minutes, then remove and transfer the cookies to a cooling rack. Wait until the cookies are completely cool to frost as desired.