In a medium bowl, whisk flour, baking powder and salt.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter and sugar together on medium-high speed until soft and fluffy, 2-3 minutes. Beat in eggs one at a time, mixing well after each addition. Blend in vanilla. With the mixer on low speed, add dry ingredients, mixing just until incorporated and evenly mixed. Cover and chill dough for 1 hour.
When ready to bake the cookies, preheat oven to 350 degrees F. Line two large baking sheets with parchment paper or silicone baking mats.
Scoop heaping tablespoons of dough into balls and place on prepared baking sheet; flatten dough balls slightly with your fingers. Repeat with remaining dough, spacing cookies 2-3 inches apart.
Bake for 10-12 minutes, or just until set. Be careful not to over-bake! The edges should be no more than very lightly browned, if at all. Let cookies cool on baking sheet for 5 minutes. Transfer to a wire rack to cool completely.
For the Frosting:
Sift confectioners’ sugar into a large bowl. Add melted butter, milk, and your desired extract to the bowl; whisk until smooth. Whisk in additional milk as necessary, 1 teaspoon at a time, until you reach your desired consistency. Separate frosting into batches, if desired, and tint each with desired food coloring.
Invert cookies into frosting and place on a large baking sheet or wire rack to let frosting set. Immediately top with sprinkles, if desired. Store in an airtight container for up to 5 days.
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