Cream the butter in the bowl of a kitchen mixer. Add the granulated sugar and beat until combined.
Scrape the sides. Add the egg and vanilla extract, and again mix until combined.
Add the all-purpose flour 1 cup at a time, beating between each new addition.
The dough should be pliable, but not sticky, once you've added all the flour. If the dough is still sticky, add more flour (about ¼ cup at a time) until the dough is no longer sticky.
Flatten the dough into discs, wrap and refrigerate for 15-20 minutes.
Once the dough is firm, roll it out into a ½" thick rectangle.
Cut the cookies with a cookie cutter and place on a parchment paper lined baking sheet.
Bake at 350F for 8-9 minutes, or until no longer shiny on top.
Cool on a rack until completely cooled before icing.
