In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.

Add the egg and vanilla extract, mixing until combined.

In a separate bowl, whisk together the flour, baking powder, and salt.

Gradually add the dry ingredients to the wet mixture, mixing until a dough forms.

Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.

Preheat the oven to 350°F (175°C).

Roll out the chilled dough on a floured surface to about 1/4 inch thickness.

Use cookie cutters to cut out sombrero shapes and place them on a baking sheet.

Bake for 10-15 minutes or until the edges are lightly golden.

Allow cookies to cool completely on a wire rack.

In a mixing bowl, combine powdered sugar, egg white, and lemon juice to make royal icing.

Divide the icing into bowls and color with food coloring as desired.

Use a piping bag to decorate the cooled cookies with the royal icing and add sprinkles.

Let the icing set before serving.