Preheat the oven to 350°F. In a stand mixer bowl, beat butter, sugar, and vanilla on medium-high speed for 3 minutes until light and fluffy.
With the mixer on low, add the egg, flour, corn starch, baking powder, and salt until just combined. Do not overmix! Fold in the sprinkles using a spatula.
Lightly flour a counter and roll the dough to about 1/4 inch thick. Cut out bunny shapes and place them on a parchment-lined baking sheet. Chill for 30 minutes, or up to 24 hours.
When ready to bake, place the cookies about 1 inch apart on a parchment-lined baking sheet. Bake for 10 minutes or until the edges are set. Cool on the pan for 5 minutes before transferring to a cooling rack.
#### For the Frosting:
In a stand mixer bowl, or using a hand mixer, beat all the frosting ingredients on medium-high speed until smooth, about 2 minutes. Add the frosting to a piping bag fitted with a round tip (or cut the end of the bag).
#### For Assembly:
Once the cookies are completely cooled, dot about 1 teaspoon of frosting on the bottom of each cookie for the tail. Dip the frosted tail in a bowl of white nonpareils.
