Preheat the oven to 350°F / 175°C. Coat a 6" cake pan with butter and sugar.
M&M Cookie Cake
In a medium sized mixing bowl, melt the butter. Whisk in both sugars, followed by the egg yolk, vanilla, and milk.
Add in the flour, corn starch, baking powder, baking soda, and salt. Fold the dry ingredients into the dough until just a few flour streaks remain.
Add in the m&m's and chocolate chips and fold the mixture together just until no flour streaks remain.
Pour the dough into the 6" cake pan and top with additional m&m's if desired. Bake for ~20 minutes, or until the edges begin to turn golden brown. The middle may slightly jiggle but that's okay - it will continue to cook even after it's taken out of the oven.
Buttercream
Beat the butter and salt with a hand mixer or stand mixer fitted with the paddle attachment until smooth.
Add in half of the powdered sugar, beat until smooth, then beat in the remaining half of powdered sugar.
Add in the vanilla, milk, and a small drop of blue food dye. Beat until combined, and add more food dye as desired.
Once the cake has cooled to room temperature, remove it from the pan. Transfer the buttercream to a piping bag fitted with your tip of choice. Frost the cake, serve, and enjoy!