01 - In a medium bowl, whisk together all-purpose flour, baking powder, and salt until evenly blended. Set aside.
02 - In a large bowl, beat the softened unsalted butter and granulated sugar together until light and fluffy, about 2 to 3 minutes using a mixer.
03 - Add the large egg and pure vanilla extract to the butter-sugar mixture, beating until fully combined.
04 - Gradually add the flour mixture to the wet ingredients, mixing just until a smooth dough forms without overworking.
05 - Split the dough into two portions, flatten into discs, wrap each in plastic, and refrigerate for at least 30 minutes for easier handling.
06 - Preheat the oven to 350°F and line two baking sheets with parchment paper.
07 - On a lightly floured surface, roll one dough disc to 1/4-inch thickness. Cut out 2-inch circles using a round cookie cutter.
08 - Arrange cookies 2 inches apart on the prepared sheets and bake for 10 to 12 minutes, until pale golden at the edges.
09 - Let cookies rest on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
10 - Whisk powdered sugar with 2 teaspoons milk and vanilla extract until a thick, spreadable consistency is achieved, adding more milk if needed. Color with food coloring if preferred.
11 - Spread or pipe icing onto cooled cookies. Immediately place edible googly eyes atop the icing before it begins to set.
12 - Allow icing to dry completely before serving or transferring cookies to an airtight container for storage.