Sift together the flour, baking powder, and salt. Set aside.
Using a stand or hand mixer, beat together the softened butter and sugar until light and fluffy, 2 to 3 minutes. With the mixer on low, add in the egg and vanilla bean paste. Mix until combined. Stop the mixer and scrape down the sides and bottom of the bowl.
With the mixer on low, slowly add the flour mixture in two additions. Mix the dough until combined. If the dough appears dry, add a splash of milk or cream (no more than a tablespoon) and mix until the dough begins to ball together.
Stop the mix and divide the dough in half. Form the dough into disks and wrap well is plastic. Refrigerate the dough for at least 2 hours or overnight.
When ready to bake, preheat the oven to 375°F and remove one disk of dough from the refrigerator. Allow the dough to come to room temperature (about 10 minutes) before rolling. Line two baking sheets with parchment and set aside.
Loosen the plastic around the dough and begin to roll it out (within the plastic) to get things started. Lightly dust your work surface with flour, unwrap the dough completely, and roll out until ¼-inch thick. Cut out cookies and move them to the lined baking sheets.
Bake for 8 to 10 minutes, or just until the cookies start to brown around the edges. Place the baking sheet on a wire rack to cool for 10 minutes, then remove the cookies. Repeat with the remaining dough.