Whisk together flour, baking powder, baking soda, and salt.
In the bowl of a stand mixer fitted with a paddle attachment, cream together butter and sugar. Add egg and vanilla extract. Mix until well combined.
Add half of flour mixture to mixing bowl. Mix on slow speed for about 10 seconds. Add milk and mix for another few seconds. Then, add remaining half of flour mixture. Mix on low speed until just combined. Scape down sides of bowl as needed to ensure thorough mixing.
Divide dough into two equal parts. Cover with plastic wrap and chill in the refrigerator for at least one hour, or overnight.
Preheat oven to 350°F. Line baking sheet trays with parchment paper or baking silicone mat. Set aside.
Work with one piece of dough at a time. Let cookie dough rest at room temperature for 15-20 minutes to gently warm up and softened. On a lightly floured work surface, roll dough to about ¼-inch thick. Cut out desired shapes using a floured cookie cutter. Transfer cut outs to prepared sheet trays.
Bake for 13-15 minutes until the edges are golden. Let cookies cool on baking sheet for a few minutes before transferring to wire racks to cool to room temperature.