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 unsalted butter and granulated sugar with an electric mixer on medium speed until light and fluffy, about 2 to 3 minutes. Add the egg and vanilla extract, beating until fully incorporated.
04 - Gradually add the dry flour mixture to the creamed butter mixture, mixing on low speed until a smooth, cohesive dough forms. Avoid overmixing.
05 - Turn the dough out onto a lightly floured surface and roll 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 cookie cutter, cut out 24 small circles for the sombrero crowns.
06 - Arrange both the large and small cookie circles on the prepared baking sheets. Bake for 8 to 10 minutes or until the edges are lightly golden. Transfer to a cooling rack and let 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 your desired food coloring.
08 - Spread colored icing over each large cookie circle to form the brim. Using a dab of icing as adhesive, stand a small cookie circle upright in the center of each brim to form the crown. Attach a gumdrop to the top of each crown with more icing.
09 - Pipe or spread additional colored icing around the edge of each brim and apply colorful sprinkles. Allow the icing to set fully before serving.