Cheesecake Mixture: In a medium bowl using a stand mixer or with a hand mixer, beat softened cream cheese and sugar on medium speed until smooth and creamy. Scrape bowl, then add egg and vanilla and beat on medium-low speed until smooth. Cover mixture and store in fridge until needed.
Prep: Preheat oven to 325°F. Grease an 8x8 pan generously with butter/cooking spray, or line with parchment.
Wet Ingredients: In a medium bowl, whisk together eggs and vanilla. In a microwave-safe bowl or glass measuring cup, melt the butter and chocolate chips together in short 10-20 second bursts until smooth, stirring frequently. Be careful not to let the mixture get too hot.
Combine: Stream the butter and chocolate mixture into the eggs and vanilla while whisking. Once smooth, add brownie mix and mix on medium-low speed with a stand mixer or with a hand mixer until no flour is visible (but be careful not to overmix). The batter will be thick.
Layering: Spread the brownie batter into the prepared pan so that it is evenly distributed. Remove the cheesecake mixture from the fridge and spread over the brownie batter in an even layer, tapping on the counter a couple times to even out the batter and pop any air bubbles. Sprinkle with the mini chocolate chips and graham cracker pieces/crumbs. Cover the top of the pan tightly with aluminum foil.
Bake: Bake for 30 minutes, rotate, then bake for an additional 35-40 minutes, checking with a toothpick to ensure doneness (once the brownies are close to being done the foil can be removed). The brownies are done when there is no wet batter remaining on the toothpick and cheesecake is just barely starting to brown around the edges, but is mostly set (you want to see very little jiggle). Let cool most of the way before slicing. Store in the fridge for up to 5 days.