Gently whisk the flour, baking powder and salt together and set aside.
Cut the softened butter into about tablespoon size pieces. Place them in the bowl of an electric mixer and cream using the paddle attachment. Then add the sugar and vanilla extract and beat for a minute or two.
Add the eggs one at a time beating after each addition. Then add the milk and beat until combined (just a few seconds). Scrape down the sides of the bowl.
Gradually add the dry ingredients and mix until combined.
Remove the dough from the mixer bowl and divide the dough in two. Wrap each half in parchment paper or wax paper. Chill for 1-2 hours.
Preheat your over to 400 F.
Roll out the dough on a floured surface using a lightly floured rolling pin. Roll the dough to about ¼ inch thickness. Use whatever shape cookie cutter you'd like.
Place the cutouts on a parchment-lined baking sheet. Sprinkle generously with sugar.
Bake for 5-10 minutes depending on the size and thickness of your cookies.
Notes
Sometimes we make these thick and bake them on the short side so they stay soft. Then we frost them.And sometimes we roll them thinner, sprinkle them with colored sugar and bake them a little longer for a nice crisp sugar cookie.