01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
03 - In a large mixing bowl, beat the softened unsalted butter and granulated sugar with an electric mixer until light and fluffy, approximately 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.
05 - Roll the dough out on a lightly floured surface to 1/4-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 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 cool completely.
07 - While the cookies cool, whisk together the confectioners' sugar, milk, and vanilla extract until a smooth, pourable icing forms. 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. Place a small cookie circle upright in the center using icing as adhesive. Top each crown with a gumdrop, securing with additional icing.
09 - Pipe or spread icing along the edge of each brim and apply colorful sprinkles. Allow the decorated cookies to set at room temperature until the icing firms before serving.