Melt the butter and chopped chocolate in a medium saucepan over medium heat.  Stir the mixture constantly for about 5 minutes.  Remove pan from heat and pour mixture into large mixing bowl for further cooling for about 10 minutes (it just needs to slightly cool, not fully).

Place your oven rack in the lower third position and preheat oven to 350 degrees.  Line the bottom and sides of a 8 inch square baking pan with parchment paper with an overhang on all sides.  This will help you to easily lift the brownies out of the pan when cool.  Set baking dish aside.

Whisk the granulated sugar into the cooled chocolate/butter mixture.  Add the eggs, one at a time, whisking until smooth after each addition.  Whisk in the vanilla.  Gently fold in the flour, cocoa powder, espresso powder, and salt.  Set mixture aside.

In your stand mixer, beat the cream cheese for 1 minute on medium high speed and beat in the sugar until combined.  Beat in egg and vanilla until combined.  Fold in the white chocolate chips with a rubber spatula.  Set aside.

Spread about half of the brownies batter into the parchment paper lined baking pan.  Try to spread the batter into each corner to make an even layer.  

Top the brownie layer with all of the cheesecake batter.  Spread the batter as best you can in an even manner, covering as much of the brownie batter as you can.

Spread the rest of brownie batter on top of the cheesecake layer and spread over the cheesecake layer as evenly and covering as much of the cheesecake as you can.

Bake in preheated oven for 35-38 minutes.  It takes 38 minutes in my oven for the perfect texture.  You will want to cook until the edges of the brownie pulls away from the the edges of the pan.  A toothpick test where only a few moist crumbs show up on the toothpick, means the brownies are ready.

Cool the brownies in the pan on a wire rack for 45 minutes.  Then cover with plastic wrap and place in the fridge for at least 2 hours.   Even after two hours, the brownies may still be a touch soft, but are cuttable. (just a little melty, but so yummy)

Enjoy these obey gooey, beyond delicious brownies!