Preheat oven to 375 degrees F. Line baking sheets with parchment paper.
In a medium bowl, stir together the flour blend, salt and baking powder. Set aside.
In a large mixing bowl, cream together the 3/4 butter and sugar. Beat in the egg and vanilla. Slowly beat in the flour mixture and blend until mixture comes together in a dough.
Generously flour a clean surface with more gluten-free flour and roll dough out to a 1/8- to 1/4-inch thickness. Cut into desired shapes using cookie cutters.
Place on prepared baking sheets and bake 6 to 8 minutes, or until just starting to brown around bottom edges.
Cool on cookie sheets at least 5 minutes before transferring to cooling rack. Cool completely before frosting.
To make frosting, beat the 1/4 cup butter and vanilla. Blend in the confectioners' sugar. Add milk, a teaspoon at a time, until desired spreading consistency is achieved. Use to frost cooled cookies.