Preheat the oven to 180 C / Gas 4. Line a 20x30cm baking tin with tin foil leaving a good amount over overhang over the sides.
Place 300g of raspberries in a food processor and blend until smooth. Press through a sieve into a clean saucepan. Dissolve the cornflour in a little cold water then add to the raspberry purée. Cook and stir for 8 to 10 minutes over a low heat until thickened. Remove from the heat and allow to cool.
Combine the biscuit crumbs and butter in small bowl and mix well. Press evenly into the bottom of the prepared baking tin.
In large bowl, beat the cream cheese until fluffy. Gradually beat in condensed milk until smooth. Add eggs, lemon juice and vanilla; mix well. Pour over prepared base.
Drop the raspberry purée mixture by spoonfuls over the cheesecake. Gently swirl with a knife to create a marbled effect.
Bake 25 to 30 minutes until centre is set then switch off the oven and allow to cool inside with the door open (this will help reduce cracking). Once cooled to room temperature, transfer to the fridge to chill for 3 hours. Lift out of the baking tin using the foil to help you then cut into slices or squares and serve topped with the remainder of the fresh whole raspberries.