Preheat your oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving a 2-inch overhang at each side.
For the brownie batter, melt chocolate and butter in a medium saucepan over low heat until smooth or melt it in the microwave in short bursts with frequent stirring. Remove from heat and stir in sugar. Whisk in eggs one at a time until it tightens up and looks thick and glossy. Stir in salt and then flour until combined. Spread batter evenly into prepared pan. Chill for 5 minutes to firm up.
For the cheesecake layer, beat soft cream cheese with sugar in a small bowl using an electric hand mixer until smooth, creamy and glossy. Beat in vanilla and egg until well combined, then mix in flour. Stir in chocolate chips.
Pour the cheesecake mixture over the brownie batter and then gently spread it out to fill the corners. Bake for 25-28 minutes until puffed and the surface looks matte. Transfer to a rack to cool then refrigerate for at least 1 hour before slicing.