Preheat oven to 375°F. Line a sheet pan with a Silpat mat (silicone baking mat)
First, in a large bowl using an electric mixer, beat the butter and sugar until it's light and fluffy.
Add a room temperature egg and vanilla to the mixture and beat until smooth.
In another bowl, combine flour, baking powder, and salt. Whisk it to combine. With the mixer on low, add your flour mixture to the butter mixture a little at a time. After it's blended together, roll the dough to 1/8 inch thickness. It may be easier to work with to separate the dough into two parts.
Dip cookie cutter in flour before cutting. Cut out the cookies and place them on a cookie sheet or sheet pan.
Bake the cookies at 375°F for 6 to 7 minutes or until cookies are lightly browned. Cool them for two minutes on cookie sheet before removing to wire rack to cool completely.