01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
03 - In a large bowl, beat the softened butter and granulated sugar with an electric mixer until light and fluffy, about 2–3 minutes. Add the egg and vanilla extract, beating until fully incorporated.
04 - Gradually add the dry ingredient mixture to the creamed butter mixture, mixing on low speed until a smooth dough forms.
05 - Roll the dough out on a lightly floured surface to ¼-inch thickness. Using a 2-inch round cookie cutter, cut out the sombrero brims. Using a 1-inch round cutter or bottle cap, cut out the sombrero crowns.
06 - Arrange both large and small circles on the prepared baking sheets. Bake for 8–10 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 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.
09 - Pipe or spread icing along the edge of each brim and apply colorful sprinkles. Allow the assembled cookies to set at room temperature until the icing firms up before serving.