01 - Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until evenly distributed. Set aside.
03 - In a large mixing bowl, beat the softened butter and granulated sugar with an electric mixer on medium speed until light and fluffy, approximately 2–3 minutes. Add the egg and vanilla extract, beating until fully incorporated.
04 - Gradually add the flour mixture to the creamed butter mixture, mixing on low speed until a smooth, cohesive dough forms. Avoid overmixing.
05 - On a lightly floured surface, roll the dough out to ¼-inch thickness. Using a 2-inch round cookie cutter, cut out 24 large circles for the sombrero brims. Using a 1-inch round cutter, cut out 24 small circles for the sombrero crowns.
06 - Arrange both large and small circles on the prepared baking sheets, spacing about 1 inch apart. Bake for 8–10 minutes until the edges are lightly golden. Transfer to a cooling rack and cool completely.
07 - While the cookies cool, whisk together the confectioners' sugar, milk, and vanilla extract until smooth and pourable. Divide the icing among separate bowls and tint each with desired food coloring.
08 - Spread colored icing over each large cookie circle to form the brim. Attach a small cookie upright in the center using icing as adhesive. Top each crown with a gumdrop, securing with a dab of icing. Decorate the brim edges with additional icing and colorful sprinkles. Allow icing to set before serving.