Begin by gathering all necessary ingredients for the cookies and royal icing.

In a stand mixer equipped with a paddle attachment, combine the granulated sugar and softened butter. Beat on medium speed until the mixture becomes light and fluffy, which should take approximately 2 to 3 minutes. Incorporate the egg and vanilla extract, continuing to mix on medium speed until fully combined, around 15 to 30 seconds.

In a separate medium bowl, whisk together the all-purpose flour, baking powder, and kosher salt until well combined.

Gradually introduce the flour mixture to the sugar and butter mixture while keeping the mixer on low speed. Mix until the ingredients are just combined, taking about 1 minute.

Divide the dough into two discs, wrap each disc securely with plastic wrap, and refrigerate for a minimum of one hour or up to one day.

When ready to bake, take the dough from the refrigerator and allow it to rest for at least 10 minutes before rolling. Preheat the oven to 350 degrees Fahrenheit (175 degrees Celsius) and line two large rimmed baking sheets with parchment paper or silicone baking mats.

On a lightly floured surface, unwrap one dough disc and roll it out to a thickness of 1/4 inch. Use your preferred cookie cutters (bunny, carrot, or egg shapes) to cut out cookies.

Arrange the cut-out cookies on the prepared baking sheets. Repeat the process with the remaining dough, re-rolling any scraps once or twice as needed.

Bake the cookies in the preheated oven until they are slightly golden, which should take between 8 to 10 minutes. After removing them from the oven, let the cookies cool on the baking sheets for 5 minutes.

Transfer the cookies to a wire rack to cool completely, which will take approximately 30 minutes.

For the royal icing, place the powdered sugar and meringue powder into a stand mixer fitted with a whisk attachment. Begin mixing on low speed until combined, which should take about 15 seconds. While the mixer is still running on low, add the water and vanilla extract. Gradually increase the speed to medium-high and continue beating until the icing reaches a smooth consistency, approximately 15 seconds. Alternatively, combine the ingredients in a medium bowl and whisk until smooth. The icing should form a ribbon that retains its shape for 1 to 2 seconds before sinking back in. Adjust the consistency by adding water if it is too thick or powdered sugar if it is too thin.

Separate 1/4 cup of the icing into small bowls for each color you wish to use (like pink, blue, yellow, and green). To prevent the icing from drying out while not in use, cover it with moist paper towels or clean tea towels.

Once the colors are prepared, transfer the icing into individual piping bags, cutting a small hole (1/8-inch) at the end or fitting with small round piping tips.

Pipe royal icing along the perimeter of each cookie to create a decorative border.

Fill in the center of each cookie with the remaining royal icing, using an offset spatula or the back of a spoon to spread the icing to the edges. Allow the cookies to stand until the icing is completely dry and set, which will take about 1 hour.

If desired, further decorate the cookies with secondary colors and designs. Allow them to set completely for an additional 30 minutes.