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, continuing to beat until fully incorporated.
04 - Gradually add the dry ingredient mixture to the creamed butter mixture, mixing on low speed until a smooth, cohesive dough forms. Do not overmix.
05 - On a lightly floured surface, roll the dough out to ¼-inch thickness. Using a 2-inch round cookie cutter, cut out large circles for the sombrero brims. Using a 1-inch round cutter, cut out smaller circles for the sombrero crowns. Re-roll scraps as needed.
06 - Arrange both large and small circles on the prepared baking sheets, spacing about 1 inch apart. Bake for 8–10 minutes until edges are lightly golden. Transfer to a cooling rack and cool completely.
07 - While cookies cool, whisk together 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 the large cookie circles to form the brims. Attach a small cookie 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 cookies to rest until icing is fully set before serving.