Line an 8×8 inch pan with your parchment paper and set aside.
In stand mixer (or lg bowl), mix together softened butter and brown sugar until fluffy for (2-3 minutes)
Add in vanilla until combined. Alternate adding flour and sweetened condensed milk until well combined (will become creamy and smooth).
Mix in the chocolate chips and M&M’s.
Press the cookie dough into the bottom of a parchment paper lined 8×8 pan and cover. Refrigerate for at least 3 hours, overnight is fine.
Flip the cookie dough out onto a cutting board or plate and carefully peel back the parchment paper. Place back in the fridge while you make the “icing”.