In a large bowl, cream butter and sugar together until smooth. Add eggs, extracts, and salt, mix well. Add the flour gradually, stirring well. Cover or wrap dough and chill for at least an hour, but preferably overnight.
Preheat oven to 400°F.
Divide dough into quarters and work with one quarter at a time, keeping the other refrigerated. Roll out on floured surface to about a 1/4 thickness. Cut into shapes with your favorite cookie cutters. Transfer cut-outs to a cool cookie sheet lined with parchment paper or a silicone baking mat.
Bake 6 to 8 minutes, or until set but not browned. Cool and decorate with royal icing.