Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
In a mixing bowl, whisk together the flour, baking powder, and salt. Set aside.
In another large bowl, cream the softened butter and granulated sugar using an electric mixer or whisk until light and fluffy, about 3-5 minutes.
Beat in the egg and vanilla extract until well combined.
Gradually add the flour mixture to the butter mixture, mixing until a dough forms.
Chill the dough in the refrigerator for at least 30 minutes for easier rolling.
Lightly flour a clean surface and roll out the chilled dough to about ¼ inch thick.
Use cookie cutters to cut out shapes and place them on the prepared baking sheets.
Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden. Remove from the oven and let cool on a wire rack.
To make the royal icing, beat the egg whites in a mixing bowl until frothy.
Gradually add powdered sugar and mix until the icing is smooth and holds stiff peaks.
If desired, add almond extract and mix well.
Divide the royal icing into small bowls and tint with food coloring as desired.
Transfer the icing to piping bags and decorate the cooled cookies with your favorite designs.
Let the icing dry completely before serving.