In the bowl of your mixer cream butter and sugar until smooth.
Beat in extracts and egg.
In a separate bowl combine baking powder with flour and add a little at a time to the wet ingredients. The dough will be very stiff. If it becomes too stiff for your mixer turn out the dough onto a countertop surface. Wet your hands and finish off kneading the dough by hand.
DO NOT CHILL THE DOUGH. Divide into workable batches, roll out onto a floured surface and cut. You want these cookies to be on the thicker side (closer to ¼ inch rather than ⅛).
Bake at 350 for 6-8 minutes. Let cool on the cookie sheet until firm enough to transfer to a cooling rack.
In a medium saucepan, combine the butter, cream, brown sugar and salt, and cook over medium heat, stirring constantly, until the mixture comes to a boil.
Remove from the heat and stir in vanilla and 1 cup powdered sugar.
Let the frosting cool to room temperature and then stir in enough additional powdered sugar to make a good frosting consistency (you may not use the whole extra cup.)