Preheat oven to 325°F (163°C). Line an 8×8-inch pan with parchment paper.
Melt butter and dark chocolate together until smooth. Let cool slightly.
Whisk in sugar, eggs, and vanilla until glossy.
Stir in cocoa, flour, salt, and espresso powder until just combined. Pour into pan.
In another bowl, beat cream cheese smooth. Add sugar, egg, and vanilla. Mix well.
Drop spoonfuls of cheesecake over brownie batter. Swirl with knife.
Bake for 35–40 minutes until edges set and center slightly jiggly.
Cool 1 hour in pan, then chill at least 2 hours before slicing.
