Preheat the oven to 350 degrees Fahrenheit. Line a 9 x 13 x 2-inch pan with aluminum foil or parchment paper for easy removal of the bars. Spray with pan spray and set aside.
In a microwave-safe bow,l or using a double boiler, melt ¾ cup butter and 6 ounces chopped dark chocolate. Stir every 30 seconds, being careful to not let the chocolate burn.
Whisk 1 ½ cups granulated sugar and½ cup packed brown sugar to the melted chocolate mixture. Then add 1 ½ teaspoon vanilla extract and 3 large eggs and mix until fully incorporated. Lastly, stir in 1 cup all-purpose flour until incorporated.
Pour the brownie batter into the prepared baking pan. Sprinkle with ¾ cup semi-sweet chocolate chips and set aside.
Make the cheesecake layer by fitting a stand mixer with the paddle attachment. Add 8 ounces cream cheese, and ¼ cup unsalted butter, to the bowl and beat on medium-high for about 2 minutes, until fluffy. Mix in 1 large egg, ½ cup granulated sugar, ½ tsp salt, and ½ tsp vanilla extract on high for another 2 minutes. Mix in 1 cup creamy peanut butter for 2 minutes.
Pour the cheesecake layer over the brownie layer and smooth it over the top so it completely covers the brownie layer. Bake for 35-40 minutes. The top and edges should be slightly golden and the center is set.
Let the bars completely cool and refrigerate for at least an hour or overnight before serving.