Add all ingredients (raspberries, water, lemon juice, sugar and corn starch) to a medium saucepan.
Turn the stove on medium heat and mix every 30 seconds or so until the mixture boils down to a liquid.
Once the mixture is simmering, turn it down to low heat and allow it to cook for another 5 minutes or until it thickens to a jelly-like consistency. Continue stirring every 30 seconds until this happens.
Pour the mixture through a sieve to remove the raspberry seeds and allow it to cool for 5-10 minutes.
Spoon the raspberry sauce over the cheesecake layer and use a butter knife to swirl it into the cheesecake. Careful not to push too far into the bars with the knife (you do not want to cut into the brownie layer).
Bake for 25 minutes or until the edges begin to set but the center is still jiggly.
Remove the cheesecake bars from the oven and allow them to cool to room temperature before moving them to the fridge to chill (for 4 hours minimum! overnight is preferred for chilling time).