Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a bowl, whisk together the flour, baking powder, and salt. Set aside.
In a separate large bowl, beat the softened butter and granulated sugar with an electric mixer until light and fluffy (about 3-4 minutes).
Add the egg and vanilla extract to the butter mixture, mixing well until combined.
Gradually add the flour mixture to the wet ingredients, mixing until the dough comes together. If the dough seems too sticky, add a bit more flour.
Divide the dough into two portions, wrap each in plastic wrap, and refrigerate for at least 30 minutes to firm up.
Once chilled, remove the dough from the fridge and roll out one portion on a floured surface to about ¼ inch thick. Use cookie cutters to cut out shapes.
Place the cut cookies onto the prepared baking sheets and bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and let cool on a wire rack.
Meanwhile, prepare the royal icing. In a mixing bowl, combine powdered sugar, egg whites (or meringue powder), and lemon juice. Beat until the mixture holds stiff peaks (about 5-7 minutes).
If using food coloring, divide the icing into multiple bowls and mix in desired colors. Transfer icing to piping bags.
Once cookies are completely cooled, decorate with royal icing as desired. Let the decorated cookies sit for several hours until the icing hardens completely.