Adapted from Peggy Porschen, Pretty Party Cakes
makes 24–30, 3-inch cookies
Cream butter and sugar using a stand mixer with paddle attachment. Add the egg, salt, and vanilla, and mix to combine. Mix in the flour. Pat dough into thick, flat disc, cover with plastic wrap and refrigerate for at least 1 hour.
Preheat oven to 365° F. Prepare rimmed cookie sheet pan with parchment paper or Silpat liner. Roll out dough on lightly floured surface to about ¼-inch thickness. Use cookie cutters to cut out cookies and place on prepared pan. If possible, put pan in refrigerator to cool cookies before baking—even 15 minutes will make a positive difference.
Bake for 8–12 minutes, until just beginning to brown around the edges. Let cool for 5–10 minutes on pan, then transfer to a wire rack to cool completely before icing.
Combine icing ingredients using a stand mixer with whisk attachment. Scrape down sides of bowl using a spatula. Whisk on high speed for a minute or two to fully combine and create a smooth consistency. If too stiff, add milk by the drop. If too loose, sprinkle in more powdered sugar.
To decorate: Use a pastry bag with a small plain tip to create an outline, then flood-fill the middle.