Add the sugar and butter to a large bowl (or the bowl of your standing mixer) and use an electric mixer to beat on high speed for about 5 minutes, or until fluffy and light.
1 ¼ cups sugar, ¾ cup butter
Add the egg, lemon zest, and vanilla, and beat again until well combined.
Add the flour, baking powder, and salt. Mix to combine, but don't over-mix. The dough will look crumbly but will hold when pressed between a finger and thumb.
2 ¼ cups all-purpose flour, ½ teaspoon baking powder, ¼ teaspoon sea salt
Divide the dough into 2 parts for easier rolling. Pat into discs and place onto a lightly floured work surface. Roll the dough out with a rolling pin to about ¼-inch (6-mm) thick.
Cut the dough into your desired shapes. Any extra dough can be re-rolled once.
Place the cut-out cookies on a baking sheet lined with parchment paper. Place the sheet in the freezer for 10-15 minutes. (If you don't have freezer space, chill in the fridge for 30-40 minutes instead.)
While the cookie shapes are chilling, preheat the oven to 350°F (180°C).
Place the cookies in the oven and bake for 8-10 minutes, or until the edges are very lightly golden. The baking time will vary depending on the size of the cookie cutters, so look for colour around the edges. Repeat for the remaining dough.
Remove the cookies from the oven and cool on the baking sheet for 5-10 minutes. Take the cookies off the tray and let them cool completely on a wire rack before icing.
To ice, divide your royal icing into several bowls (one bowl for each colour) and whisk in food colouring until it reaches your desired shade. You can dip the cookies or pipe and flood, whatever you'd like. Top with sprinkles and dry before storing.