Preheat oven to 350℉. Line two cookie sheets with parchment paper.
In a stand mixer (or large bowl), cream the butter until smooth. Add sugar and beat until light and fluffy. Add eggs one at a time, mixing well after each. Add vanilla and almond extracts and mix to combine.
Slowly mix in flour and baking powder until a soft dough forms.
Scoop a large amount (about 1/4 cup) of dough and roll into a ball. Place onto parchment-lined sheet. Flatten each ball using the bottom of a drinking glass or cup.
Bake 9-11 minutes until edges are set and center is still soft. Let cool completely on a wire rack.
Meanwhile, prepare the icing. Beat softened butter on medium speed until creamy. Gradually add powdered sugar and mix until smooth. Stir in almond extract and 1 tbsp milk to reach a spreadable consistency. If icing is too thick, add additional milk if needed.
Smooth icing onto cookies by the spoonful. Cover, and chill in fridge about 30 minutes prior to serving.
