In a medium saucepan over medium heat, combine raspberries and sugar, cooking for 5-7 minutes until thickened. Optionally, add lemon juice. Strain to remove seeds and set aside to cool.

Preheat your oven to 325°F (163°C). Line an 8x8 inch baking pan with parchment paper.

Melt butter and chocolate in a heatproof bowl over a double boiler, stirring until smooth. Let cool slightly.

Combine cooled chocolate mixture with sugar, then add eggs one at a time, mixing well. Incorporate vanilla, then sift in flour, cocoa powder, and salt; mix gently.

In a separate bowl, beat cream cheese with sugar until smooth; add in one egg and mix until fully integrated.

Spread half of brownie batter in the prepared pan, doling the cheesecake mixture on top, followed by spooning the cooled raspberry sauce.

Gently swirl the raspberry sauce into the cheesecake and brownie layers using a toothpick.

Bake for 35-40 minutes, checking for set edges and a clean toothpick.

Cool completely in the pan on a wire rack, then refrigerate for at least 2 hours before cutting.