Preheat oven to 180 degrees celsius (fan-forced). Grease and line a 20cm round cake tin with baking paper and set aside.
Insert the butterfly into the Thermomix bowl. Add the softened butter and brown sugar and cream for 1 minute, Speed 6 (scraping down the sides occasionally) or until pale and creamy.
Reduce to Speed 2 and add the egg and vanilla extract. Remove the butterfly.
Add the plain flour, bi-carbonate soda and sea salt and mix on Speed 4, 10 seconds. Scrape down the sides of the bowl and repeat for a further 5 seconds.
Add the chocolate chips and M&Ms and mix on Reverse, Speed 3, 10 seconds (using the spatula to help mix).
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 icing, place the icing sugar into the TM bowl and mix for 10 seconds on Speed 9.
Add the butter, milk, vanilla extract and food colouring to the bowl. Mix for 30 seconds on Speed 4.
Pipe the frosting over the outside of the cookie cake and decorate with sprinkles (optional).