Gluten-Free Sugar Cookies

Whisk flour, baking powder, and salt together in a bowl.
Beat white sugar, 3/4 cup butter, and 1 teaspoon vanilla extract together in a bowl using an electric mixer; beat in eggs, 1 at a time, until the mixture is smooth.
Mix the butter mixture into the flour mixture and form dough into a ball.
Wrap the ball with plastic wrap and refrigerate for 1 hour.
Preheat the oven to 325 degrees F (165 degrees C).
Roll the dough onto a lightly floured surface and cut into shapes using cookie cutters.
Arrange cookies on a baking sheet.
Bake in the preheated oven until the edges begin to brown, about 10 minutes.
Cool cookies on the baking sheet for 2 minutes before transferring to a wire rack to cool completely.
Beat cream cheese, 1/4 cup butter, and 1 teaspoon vanilla extract together in a bowl using an electric mixer until smooth.
Slowly beat confectioners' sugar into the cream cheese mixture until the icing is smooth; spread onto cooled cookies.