Preheat oven to 180 degrees celsius (fan-forced). Grease and line a 20cm round cake tin with baking paper and set aside.
Cream the butter and brown sugar on high speed with hand-held beaters or a stand mixer in a large mixing bowl until pale and creamy.
Add the egg and vanilla extract and beat well.
Sift over the plain flour, bi-carbonate soda and sea salt and beat on low speed until just combined.
Stir through the chocolate chip and M&Ms.
Bake for 25 minutes or until just golden. Remove from the oven and allow to cool in the tin before transferring to a wire rack to cool completely before frosting.
To make the frosting, beat the butter in a bowl until pale and fluffy (approximately 5 minutes).
Slowly add the icing sugar mixture, milk, vanilla extract and food colouring and continue to beat until smooth and creamy.
Pipe the frosting over the outside of the cookie cake and decorate with sprinkles (optional).