Preheat the oven to 350 degrees F (175 degrees C).

Combine flour, butter, and confectioners' sugar in a large bowl. Beat with an electric mixer until creamy and smooth, about 10 minutes. Drop teaspoonfuls of cookie dough onto rimmed baking sheets. Decorate cookies with maraschino cherry pieces.

Bake in the preheated oven until bottoms are lightly browned, 15 to 18 minutes. Transfer to wire racks to cool completely.