Preheat oven to 350 degrees. Line two large baking sheets with parchment paper.
With an electric mixer, cream together the 1 cup butter and 1 cup sugar until light and fluffy. Mix in the 2 eggs, 1/2 teaspoon vanilla and 1/2 teaspoon almond extract.
Add the 2 teaspoons baking powder and 1/2 teaspoon salt and mix to combine. Gradually add the 3 cups flour, mixing until thoroughly combined.
Roll 1/4 cup of dough into a ball and place on the prepared baking sheets, at least 2 inches apart.
Dip the bottom of a drinking glass in sugar and flatten the cookie to about 1/2 inch thickness. The sides of the dough should squish out around the bottom of the glass to form an edge. Repeat with remaining dough, placing 6-8 cookies per baking sheet.
Bake for 8-10 minutes, or until cookies are just set and starting to brown on the bottom. Do not overbake. Transfer to a wire rack to cool completely.
Meanwhile, make the frosting: Beat the 1/2 cup butter with an electric mixer until light and fluffy. Mix in the 1 teaspoon almond extract and Pinch of salt.
Add the 3 cups powdered sugar, 1 cup at a time, and beat until smooth. Add 2-3 tablespoons milk, 1 tablespoon at a time until frosting reaches desired consistency. Color with pink food coloring, if desired.
Store in an airtight container in the refrigerator. Serve chilled.