Preheat oven to 350F. Line 13x9 pan with foil (enough so that foil hangs over 9" sides--this will make it easier to lift out of the pan and cut once the squares are finished)
In food processor, pulse Oreos and melted butter until combined.
Press Oreo/butter mixture evenly into the bottom of prepared pan with the back of a spoon.
In KitchenAid (or with hand mixer) cream butter and sugars.
Add egg and egg yolk until well-combined.
Stir in vanilla.
In separate, medium-sized bowl combine flour, pudding mix, baking powder, corn starch and salt.
Gradually, with mixer on low-medium speed, stir flour mixture into butter mixture.
Stir in chocolate chips and M&Ms. Transfer to another bowl and set aside, clean your KitchenAid bowl and paddle to make the cheesecake batter.
Take approximately ½ of the cookie dough and scatter approximately ½"-1 ½" pieces over the crust in the prepared pan. Set aside.
In KitchenAid (or with hand mixer), cream cream cheese. Add sugar and beat on medium-speed until well-combined.
Add in sour cream, stirring until just combined.
Stir in vanilla.
With mixer on low speed, add in eggs one at a time, stirring until just combined.
Pour cheesecake batter into prepared pan over cookie dough.
Scatter the remaining cookie dough (you will probably have to break off pieces of the dough to the desired size) over the top of the cheesecake batter, pressing slightly into the batter.
Transfer to oven and bake for 45-50 minutes (edges should be set, center may jiggle slightly but should spring back if lightly touched and should not be liquid).
Allow to cool on stovetop for at least one hour before transferring to refrigerator and allowing to chill for at least 6 hours before cutting and serving.