Preheat your oven to 350°F.
Line an 8-inch square baking dish with parchment paper, allowing excess to overhang for easy removal later. Spray with non-stick cooking spray.
In a microwave-safe bowl, combine the butter and 1 cup of chocolate chips. Microwave in 30-second intervals, stirring between each, until melted and smooth.
Mix in 1/2 cup sugar, then beat in 2 eggs and 1 teaspoon vanilla extract until well combined.
Fold in the flour, cocoa powder, and salt until just combined, being careful not to overmix.
Transfer a quarter of the brownie batter to a separate bowl and set aside.
Fold the remaining 1/2 cup of chocolate chips into the main brownie batter, then pour into the prepared baking dish, smoothing the top.
In another bowl, beat the softened cream cheese with 1/4 cup sugar until creamy. Beat in 1 egg and 1/2 teaspoon vanilla extract until smooth.
Pour the cheesecake mixture over the brownie layer, spreading evenly.
Dollop the reserved brownie batter over the cheesecake layer. Use a knife to swirl the two batters together, creating a marbled effect.
Bake in the preheated oven for about 30 minutes, or until a toothpick inserted into the center comes out mostly clean with a few moist crumbs attached.
Allow the brownies to cool in the pan on a wire rack before lifting out using the parchment paper overhang. Slice into 12 bars.