Preheat oven to 325 degrees. In a large mixing bowl, sift together flour, salt, and baking powder. Set aside. Place butter and sugar in the bowl of an electric mixer fitted with the paddle attachment, and beat on medium speed until mixture is light and fluffy. Beat in egg and vanilla. Add flour mixture all at once; beat on low speed until mixture comes together to form a dough.
Turn dough out onto a piece of lightly floured parchment paper; using a rolling pin, roll out to 1/8 inch thick. Using a 3 1/4- inch round cookie cutter and a 2-inch star cutter, cut out an equal number of rounds and stars. Remove scraps from around cutters as you work. Transfer parchment paper with the dough shapes to a baking sheet. On a lightly floured work surface, reroll scraps, and cut out shapes; transfer to baking sheet with other cookies. Place in refrigerator at least 15 minutes.
Remove baking sheet from refrigerator, and arrange cookies so that they are at least 1/2 inch apart. Place in oven, and bake until edges are just starting to brown, about 20 minutes. Transfer baking sheet to a wire rack; using the blunt end of a skewer, immediately poke a hole in top center of each round cookie for the ribbon, if desired. Let cool completely.
Place 1/3 cup royal icing in a small bowl, and tint with the color you wish to use for piping dots; add water as needed, but keep it fairly thick. Divide remaining royal icing into two small bowls, and tint them the remaining two colors; add water, making these slightly thinner for covering cookies. Place each tinted icing in a piping bag fitted with an Ateco #3 round tip.
Using the thinner icings, outline and fill in round cookies with one color; use the other color to outline and fill in the stars. Let iced cookies set, at least 1 hour. Pipe dots around edges of round cookies with thicker icing. Sprinkle with sanding sugar, and shake off excess. Pipe a small dab of icing on the back of each star; attach stars to centers of round cookies. Let icing set, at least 1 hour. Thread thin ribbons through the poked holes and tie, if desired. Serve, or store in an airtight container at room temperature for up to 3 days.