Preheat the oven to 350°F. Lightly grease a 9-inch square baking pan with butter or baking spray and line it with parchment paper.

In a large microwave-safe bowl, combine the butter and 1 cup of chocolate chips and microwave in 20-second intervals, stirring between each one, until fully melted and combined, about 2 minutes. Whisk in the cocoa powder. Add the sugar, eggs, egg yolk, coffee, and vanilla, and whisk until well combined.

Add the flour and salt, and stir together with a spatula until just combined. Reserve ½ cup of brownie batter in a small bowl. Stir the remaining ⅓ cup of chocolate chips into the remaining batter, and spread the batter into the prepared pan.

Bake for 20 minutes for super fudgy brownies or 30 minutes for more cakey brownies. Meanwhile, stir the hot water into the reserved batter. The batter should still be thick but slowly pour off a spoon. Add more water if needed.

While the brownie base is baking, make the cheesecake topping by placing the cream cheese, sugar, and salt in a large mixing bowl. Beat with a hand mixer or a stand mixer fitted with the whisk attachment on medium speed until very smooth and light, about 2 minutes.

Reduce the speed to low and add the eggs in one at a time. Scrape down the bowl, then beat in the vanilla. Carefully pour the cheesecake topping over the par-baked brownie base. (No need to cool the brownie first.)

Dollop the reserved brownie batter over the cheesecake topping. Using a skewer or the tip of a knife, carefully swirl the batter through the cheesecake mixture.

Continue baking for 10 minutes.

Reduce the oven temperature to 325°F and bake for another 20 to 25 minutes or until the cheesecake topping is puffed around the edges and the center wobbles slightly. Place the pan on a wire rack to cool completely. Refrigerate for 1 hour before slicing.