Prepare the Cookie Dough
In a large bowl, cream together the softened butter and sugar until light and fluffy.
Beat in the eggs and vanilla extract.

Mix Dry Ingredients
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add to the wet ingredients, mixing until just combined.

Shape and Bake
Preheat the oven to 350°F (175°C).
Scoop dough into balls and place on a lined baking sheet, spaced about 2 inches apart.
Bake for 12 minutes, or until edges are lightly golden. Do not overbake.

Make the Butter Glaze
While the cookies bake, combine the butter, powdered sugar, milk, and vanilla in a small saucepan over low heat. Stir until smooth.

Glaze the Cookies
While cookies are still warm, brush generously with the butter glaze. Allow to set slightly before serving.