Preheat the oven to 350˚F (180˚C). Line baking sheets with parchment paper.
In a large bowl, combine the flour, baking powder, and salt. Mix with a fork.
In a separate large bowl, cream together the butter and sugar with an electric hand mixer for 3-5 minutes, until butter and sugar are fully combined, but before the mixture becomes fluffy. Add the egg and vanilla, and beat to incorporate. Add the flour mixture and mix until just combined, but crumbly. Finish mixing with your hands until the dough comes together in a ball.
Transfer the dough to a floured surface. Lightly flour the top of the dough and roll out to about ¼-inch thick. Use cookie cutters of your choice to punch out cookies. Place the cookie cut-outs on the prepared baking sheets.
Bake for 10 minutes, until lightly browned around the edges. Let cool completely.
Decorate the cookies with royal icing and let dry completely, at least 3-4 hours or overnight.