Cream butter and sugar until light and fluffy, 2 minutes, scraping sides of bowl occasionally. Add in egg and extract and mix to incorporate. To measure flour, spoon into cup and level off with a knife.

In a separate bowl combine flour, baking powder and salt.  Slowly add flour mixture to butter mixture and mix until completely combined.  Dough will look crumbly, but keep mixing with a stand mixer until it turns into a soft cohesive dough. Refrigerate at least one hour. Preheat oven to 350F, then roll out and cut shapes or use preferred method:

Gather half of dough and form into a large ball.  Place on a silicone baking mat (or a large piece of plastic wrap) and press down gently.  Place a sheet of parchment paper on top of dough and roll on top of parchment into an even layer about 1/4 inch thick, or more for thick cookies. 

Pick up silicone mat and flip entire thing over.  Peel off silicone baking mat so you are left with sheet of parchment with rolled dough on top.  Place parchment-lined dough on a baking sheet and place in fridge or freezer.  Repeat with remaining dough.  (See recipe tutorial for photos of this process.)  Refrigerate 20 minutes or freeze for 10.

Remove chilled dough, cut into shapes and bake 8-12 minutes depending on thickness of cookies.  Baking time is a personal preference.  Watch for edges and tops to be set. For thick, soft cookies, remove from oven before pan is golden brown.