Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking soda and salt. Set it aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, sugar and brown sugar until light and fluffy, about 2 minutes. Add the egg then beat in the peanut butter, milk and vanilla extract.
Add the flour mixture to the stand mixer, beating just until combined.
Scoop out 1 1/2-tablespoon portions of the dough and roll it into balls.
Add each of the sanding sugars to individual bowls. Roll a third of the cookie balls into each color of the sanding sugar and arrange them on the baking sheets, spacing them 2 inches apart.
Bake the cookies until they are set, 6 to 8 minutes, then remove them from the oven and let them cool for 2 minutes.
Press three Mini Cadbury Eggs into the center of each cookie. Let the cookies finish cooling then serve.