Start with making the brownies:
Preheat the oven to 350F/175C. Line a 8×8-inch baking pan with parchment paper.
In a large heat-proof bowl, put the chocolate and butter and melt in the microwave in 20 second-intervals, stirring in between each interval, until melted (or set it over a saucepan of simmering water, stirring occasionally). Add the sugar and whisk until combined. Add the eggs, one at a time, and whisk just until combined. Add the vanilla and stir. Do not over mix. Sift the flour and salt over the chocolate mixture and fold, using a rubber spatula, just until mixed.
Set aside ½ cup of the batter and pour the rest into the prepared pan. Smooth the top.
To make the cheesecake:
Using a mixer, beat the cream cheese on medium speed until smooth. Add the granulated sugar and beat just until light and smooth. Scrape the sides and bottom of the bowl as needed. On low speed, beat in the egg and vanilla extract until combined. Add heavy cream and beat just until combined. Pour into the pan, on top of the brownie batter.
Take the reserved ½ cup of brownies batter and spoon dollops on top of the cheesecake batter. With a knife or a skewer, swirl the two batters together, to get a marble effect.
Bake for 30-40 minutes until the cheesecake filling is set, slightly puffed and just beginning to brown. A toothpick inserted into the center of the brownies should come out with a few moist crumbs. Let the brownies cool completely and then refrigerate them for at least one hour until they are firm enough to cut. Once firm, lift them out of the pan using the parchment paper and cut into squares.