Preheat oven to 350 degrees. Line a 9 x 13 pan with nonstick cooking spray and parchment paper and set aside.
In a large pot over medium-low heat, melt butter, oil, chocolate, and cocoa together until fully melted and smooth. Remove from heat.
Pour in sugar and vanilla extract. Add in eggs, 1 at a time, stirring vigorously before the next addition. After all four eggs have been mixed in, the batter should be thick and smooth without that granular look to it. Add in the remaining dry ingredients and stir gently until just combined. Do not over mix.
Fold in milk chocolate chips if using and pour batter into prepared pan. Smooth the top. Set aside.
In a separate bowl, mix cream cheese together with sugar, vanilla and egg until completely smooth.
Dollop the top of the brownies with the cheesecake mixture and use a butter knife or wooden skewer to swirl the cheesecake into the brownie batter. If your cream cheese was too warm, your cheesecake mixture might be a little loose (like mine shows in the photos). If this is the case, simply drizzle across the top and drag it through using a butter knife or wooden skewer.
Bake 30-35 minutes. Cool at least 15 minutes before cutting and serving. I prefer to cool my brownies to room temperature, then refrigerate before cutting and serving. I just prefer them cold :)