In the bowl of a stand mixer or using a hand mixer, beat together softened butter and granulated sugar until the texture becomes light and fluffy. Incorporate the vanilla extract and egg, blending until the mixture is fully unified. In a separate bowl, whisk together the all-purpose flour, baking powder, and table salt. Gradually incorporate the dry ingredients into the creamed mixture until a smooth dough forms.

Divide the dough in half and place each portion onto plastic wrap. Flatten into disks, cover tightly, and refrigerate for a minimum of 2–3 hours (or up to 5 days). Once chilled, preheat the oven to 350°F (175°C) and prepare a baking sheet with parchment paper or leave it ungreased.

Generously flour a clean surface, place one dough disk down, and roll it to a thickness of ⅛ inch for crisp cookies or ¼ inch for a softer texture. If the dough begins to crack, allow it to rest at room temperature for 10–15 minutes before rolling again.

Use cookie cutters to shape the dough, and gently transfer each cookie to the prepared baking sheet, spacing them about 1 inch apart. For undecorated cookies, sprinkle sanding sugar before baking if desired. Bake for 8–10 minutes, or until the edges exhibit a slight golden hue. Cool entirely on the baking sheet before decorating.

In a mixing bowl, stir together sifted powdered sugar, 2 tablespoons milk, corn syrup, and vanilla extract until well blended. Adjust the consistency by adding milk one teaspoon at a time if too thick, or more sugar if overly thin. If desired, divide and tint the icing using gel food coloring.

Transfer the icing to a piping bag fitted with a tip or to a Ziploc bag with the corner snipped. Pipe designs onto cooled cookies and adorn with sprinkles or candies if preferred. Allow several hours for the frosting to set completely before stacking or storing.