Preheat oven to 350°F. Line a baking sheet with parchment paper.

Whisk together flour, baking powder, and salt.

In a large bowl, beat the butter and sugars until light and fluffy. Mix in egg and vanilla.

Add the dry ingredients to the butter mixture, mixing until combined.

Roll the dough into balls. Flatten the balls slightly. Place on the baking sheet at least 2 inches apart.

Bake the cookies for about 8-10 minutes. Let cookies rest on the baking sheet for 5 minutes and then transfer to a wire rack to cool completely.

To make the frosting, mix the butter until creamy and smooth. Mix in powdered sugar and vanilla.

Using a piping bag or a spoon, frost the bottoms of half the cookies, then sandwich with another cookie.