Make the cookies: Sift flour, baking powder, and 1/2 teaspoon salt into a large bowl.
Beat butter and granulated sugar with a mixer on medium-high
speed until pale and fluffy, about 3 minutes. Beat in eggs, 1 at a time. Reduce speed to low. Add flour mixture, then vanilla. Refrigerate dough, wrapped in plastic wrap, for at least 1 hour.
Preheat oven to 325 degrees. Roll out dough to a scant 1/4-inch thickness on a lightly floured surface. Cut out cookies using a 5-inch lamb cookie cutter (fancyflours.com), rerolling scraps once. Transfer to a baking sheet, and refrigerate until firm, about 30 minutes. Bake until edges just start to brown, 10 to 12 minutes.
Transfer cookies to a wire rack, and let cool completely.
Decorate the cookies: Transfer icing to a pastry bag fitted with a small round tip. Pipe an outline of icing around the edges, then "flood" each cookie with more icing to cover. Sprinkle with sanding sugar. Let cookies dry completely before tying a pink or blue ribbon around each lamb's neck if desired.
