Prepare the Dough. In a medium bowl, whisk together flour, baking powder, and salt. Set aside. In a large mixing bowl, cream softened butter and granulated sugar until light and fluffy, about 2–3 minutes. Beat in the egg, vanilla extract, and milk until fully combined. Gradually add the dry ingredients to the wet ingredients, mixing until a soft dough forms.
Chill the Dough. Cover the dough with plastic wrap and refrigerate for at least 1 hour. This step helps the cookies maintain their shape during baking.
Shape and Bake. Preheat your oven to 375°F and line baking sheets with parchment paper. Roll the dough into 1-inch balls and place them 2 inches apart on the baking sheets. Flatten each ball slightly with the bottom of a glass. Bake for 8–10 minutes or until the edges are set but the centers are still soft. Avoid overbaking! Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.