In a large bowl, cream the softened butter and powdered sugar together until light and fluffy, about 2-3 minutes. Add the vanilla extract and mix until combined.

In a separate bowl, whisk together the all-purpose flour and cornstarch. Gradually add the dry ingredients to the butter mixture, mixing until a soft dough forms.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Take small portions of dough and roll them into log shapes, about 2 inches long and ½ inch thick. Place the logs on the prepared baking sheet, spacing them about 1 inch apart.

Bake the cookies for 12-14 minutes, or until the edges are just lightly golden. Be careful not to overbake, as the cookies should remain pale. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

In a small bowl, whisk together the powdered sugar, melted butter, milk, and vanilla extract until smooth. The icing should be thick but pourable. If it’s too thick, add a little more milk, one teaspoon at a time, until it reaches the right consistency.

Once the cookies are completely cool, drizzle or spread the icing over the tops of the cookies. While the icing is still wet, sprinkle with chopped nuts or festive sprinkles for garnish.