For the Sugar Cookies:

1. 1. Preheat your oven to 350°F (175°C).
2. 2. In a large mixing bowl, cream together softened butter and granulated sugar until light and fluffy.
3. 3. Beat in one large egg and vanilla extract until combined.
4. 4. In another bowl, whisk together all-purpose flour and baking powder.
5. 5. Gradually add the dry ingredients to the wet mixture, stirring gently until a smooth dough forms.
6. 6. Roll out the dough on a lightly floured surface to about a quarter-inch thickness.
7. 7. Cut into desired shapes using cookie cutters and place on parchment-lined baking sheets.
8. 8. Bake for about 8-10 minutes or until edges are lightly golden.
9. 9. Let cookies cool completely before decorating.

For the Royal Icing:

1. 1. In a mixing bowl, combine powdered sugar, egg whites (or meringue powder), and lemon juice.
2. 2. Mix until smooth and glossy; adjust consistency if necessary by adding water or more powdered sugar as needed.
3. 3. Once cookies are cool, pipe or spread royal icing onto cookies to decorate.