In a large bowl, cream butter and sugar until smooth. Beat in eggs and vanilla. Stir in flour, baking powder, and salt. (NOTE: If dough is dry add a tablespoon of water at a time and blend well until you get a dough that holds together well, but is not wet or sticky.)
Chill dough at least one hour or overnight.
Preheat oven to 400°F.
Roll out dough on floured surface, 1/4 to 1/2 inch thick. Cut into shapes or rounds. Place cookies 1 inch apart on ungreased parchment-lined baking sheets.
Bake 6 to 8 minutes. Let cool on pan for 5 minutes, then transfer to cooling racks.
NOTE: Baking time may vary. Watch cookies closely after 6 minutes but first pan may take up to 10 minutes before ready.
NOTE: To ensure consistent bake time for all pans of cookies, once oven reaches 400°F wait 20 minutes before baking first pan to ensure heat gets evenly distributed in oven.
*You can substitute the same amount of any of the following for maple sugar in recipe: date sugar, muscavado, sucanat, or coconut sap sugar.