Preheat the oven to 350°F. Grease or line 2 baking sheets or cookie sheets with parchment paper.

Whisk together in a medium bowl:

Beat in a large bowl, or in a stand mixer with the paddle attachment, until creamy:

Beat in:

Add the flour mixture to the butter-sugar mixture in two parts, alternating with:

Use the dough immediately or refrigerate for up to 4 days. Let the dough come to room temperature before rolling. Divide the dough in half. Cover one half with plastic wrap and roll out the other half between two pieces of parchment paper to ¼ inch thick. Cut out cookies using a 4- to 5-inch-tall cutter and arrange 1 ½ inches apart on the prepared baking sheets. Gather the scraps and reroll one time to cut out more cookies. Bake until the edges of the cookies have just barely darkened, 8 to 10 minutes, switching oven racks and rotating the sheets halfway through. Let cool on the sheets for 2 to 3 minutes, then transfer to a wire rack to cool completely. Decorate the cooled cookies with:

Pipe the icing using a pastry bag fitted with a ⅛-inch round tip, and apply the icing with a wooden pick or a small knife for additional garnishes—caps, hair, mustaches, belts, etc.