Preheat your oven to 350°F (175°C) and grease a 9-inch springform pan, lining the bottom with parchment paper. Melt unsalted butter in a medium bowl, then mix in granulated and brown sugars until fully combined. Once slightly cooled, add in eggs and vanilla extract. In a separate bowl, whisk together flour, cocoa powder, and salt, then fold these dry ingredients into the wet mixture. Stir in semi-sweet chocolate chips, pour the batter into the prepared pan, and bake for 25-30 minutes, until a toothpick comes out with a few moist crumbs. Cool the brownie base completely before proceeding.

Reduce the oven temperature to 325°F (160°C) for the cheesecake layer. In a large mixing bowl, beat cream cheese until it’s smooth and creamy. Gradually mix in granulated sugar, followed by eggs, vanilla extract, brewed coffee, and flour, ensuring everything is well combined without overmixing. Carefully spread this luscious coffee cheesecake mixture over the cooled brownie base, making sure it's even. Bake for 50-60 minutes, allowing the edges to firm up while the center remains slightly jiggly for a perfectly creamy finish.

After baking, turn off the oven and leave the cheesecake inside to cool for about 1 hour; this helps prevent cracking. Once cooled, transfer the cheesecake to the refrigerator and allow it to chill for at least 4 hours, though overnight is ideal.

To serve your delightful Coffee Brownie Cheesecake, carefully release it from the springform pan and slice it using a warm, clean knife for smooth edges. Feel free to garnish with whipped cream, chocolate shavings, or even a few coffee beans.