In a medium-size mixing bowl, whisk together softened butter, sugar, egg, and vanilla until light and fluffy. Add flour mixture, stirring with a wooden spoon until just combined, then add the sprinkles. Scoop cookie dough and refrigerate for 1 hour.
Place cookie dough on a lined baking sheet 2 in” apart. Preheat oven to 350F & bake for 10-12 minutes.
In a stand mixer, start creaming together softened butter & icing sugar on low – slowly adding the sugar, & eventually vanilla & milk. Mix until light and fluffy. Transfer to a piping bag. Add food colouring if desired.
Place one cookie facedown on a plate, pipe buttercream to cover the whole cookie. Place another cookie facing up on top and give a little squeeze.