Mix together the flour, salt and baking powder in a bowl. In a separate bowl, cream the butter and sugar with an electric mixer until it becomes light and fluffy. Add the milk to the mixture along with the egg and vanilla, and mix well. Then slowly add the flour mixture until it is just combined.
Shape the dough into a ball, then divide it into two balls. Wrap them in plastic wrap. Place one in the refrigerator to chill for 1 hour, and place the other ball of dough in the freezer to save for later use.
Lightly dust some flour onto your countertop, and roll the dough out until it is ¼ inch thick. Using a 2-inch circle-shaped cookie cutter, cut out circle shapes. Place these on a baking sheet lined with parchment paper, and bake for about 10 minutes at 350F, until lightly golden. Transfer these to cooling racks and allow to fully cool.