Preheat the oven to 180 C / Gas 4. Lightly grease and line the base of a 20cm / 8 inch round sandwich tin, that has a springform surround. Place into a fridge to chill, whilst you prepare the biscuit crumb base.
Place the biscuits and pecan nuts into a food processor and whizz until they reach a smallish crumb. Take from the food processor, place into a bowl and then add the 1 teaspoon vanilla extract and melted butter. Mix well until all the crumbs are decently coated with liquid.
Get the lined cake tin from the fridge. Tip the crumb mixture into the pan, then press the mix into the base and all the corners until even and nicely pressed down. Put the lined tin back into the fridge to harden.
Now measure out all the ingredients for the filling except the raspberries or other fruit. Put all of these into a mixing bowl or processor and mix or process until smooth and well mixed together. It is worth scraping down the sides a couple of times with a spatula to make sure that everything has mixed thoroughly.
Go and get the crumb base from the fridge, then evenly place a handful of fresh raspberries over the biscuity base. Now pour over the cream cheese mix gently. Afterwards, I then go over the raspberries to try and even them out a bit; do not overdo this tidying up, but you do not want someone to get all the raspberries, while someone else goes without – that would be really bad form. Sprinkle delicately 4 pinches of mixed spice over the top of the cheesecake filling.
Put centrally into the oven and bake for 25 to 30 minutes until just set. Remove from oven and leave to cool completely, then remove the springform outside ring of the cake and place the cake (still on its base) into the fridge to chill through.
While it is cooling, it is time to make the raspberry coulis. Place the raspberries into a pan, together with the lemon juice, water and sugar. Bring to the boil and simmer with the lid on for 10 minutes. Leave to cool thoroughly. While it is cooling, check the sweetness of the raspberries and adjust sugar level if necessary as they can be really tart.
Process the raspberries throughly to a smooth paste either with a hand held processor or in a larger processor. Now sieve the raspberry paste into a jug or bowl to remove the seeds. You will need to squish the juice through with a tablespoon. Put into the fridge to cool.
Before serving remove from the fridge to warm up a little. Cut into smallish slices and place onto a plate, then drizzle over some of the raspberry coulis.