Prepare the dough: In a large bowl, beat the butter, sugar, and vanilla extract until light and creamy. Add the egg and continue beating until fully combined.
Stir in the dry ingredients: In the same bowl, add the flour, baking powder, and salt. Use a spatula to combine the dry and wet ingredients until a smooth dough forms.
Chill the dough: Place the dough on a piece of plastic wrap and flatten it into a rectangular shape. Wrap it tightly and place it in the freezer for at least 2 hours, preferably overnight.
Roll and cut: Remove the dough from the freezer and place it on a lightly floured surface. Roll it out with a rolling pin until it is approximately 0.6 cm (1/4 inch) thick. Use Easter Bunny-themed cookie cutters to shape them.
Chill and bake: Place the cookies on a baking sheet lined with parchment paper. If desired, refrigerate again for 5 minutes or freeze briefly to retain their shape. Bake in a preheated oven at 350°F (175°C) for 8-9 minutes, or until the edges are lightly golden. Remove from the oven and let cool completely before decorating.
Icing Preparation: In a bowl, combine the powdered sugar and meringue powder, then gradually add 3 to 4 tablespoons of water while beating at medium speed. Beat for about 7 minutes or until you reach a ribbon consistency. If the icing is too thick, add more water, one teaspoon at a time, until you reach the desired consistency.
Color and Decorate: If using different colors, divide the icing into bowls. For black icing, use a small portion and gradually add black food coloring until you get the desired shade. For pink, use red food coloring. Transfer the icing to piping bags and decorate the cookies as desired. Use a toothpick to add details or secure the design.
Let Dry: Let the decorated cookies dry completely before storing or serving.