Preheat the oven to 180C/160C Fan/Gas 4.
For the pastry base, rub the flour into the butter until it resembles breadcrumbs. Mix in the icing sugar.
Whisk the eggs and milk together in a separate bowl and add to the flour mixture. Use your hands to bring the dough together. Wrap in cling film and transfer to the freezer for 10 minutes.
On a lightly floured work surface, roll out the pastry as thinly as possible (ideally 3mm thick).
Line the 3 tins with the pastry, making sure to leave some extra in case it shrinks (leave any excess pastry upright not hanging over the sides as it could be difficult to trim later). Prick the bases with a fork and chill the filled tins for 15 minutes in the fridge.
Line the inside of the tins with baking paper and fill each tin with baking beans. Place the tins on baking trays. Blind bake the pastry shells for 15 minutes. Remove the baking beans and leave the pastry to cool in the tins.
Reduce the oven temperature to 150C/130C Fan/Gas 2.
For the cream cheese filling, mix the cream cheese and sugar in a large bowl until incorporated. Add the soured cream, eggs, egg yold and flour. Mix gently to avoid incorporating excess air and pour the mixture into the pastry cases leaving a small lip at the top which will be filled with sauce later.
Scatter the stem ginger over the surface of the 20cm/8in cheesecake, the lemon zest on the 18cm/7in cheesecake and swirl the vanilla bean paste on the 15cm/6in cheesecake. Place all the tins on the middle shelf of the oven and bake the 15cm/6in cheesecake for 30 minutes and the 2 larger ones for 45 minutes, or until each cheesecake is set with a slight wobble in the centre. Leave them to cool in the tin.
For the ginger beer topping, heat the cream until just boiling then pour it over the chocolate. When melted, stir in the stem ginger syrup. Once it has cooled a little, pour over the 20cm/8in cheesecake. Cool in the fridge or freezer.
For the lemonade topping, heat the cream until just boiling then pour it over the chocolate. When melted, stir in the lemon extract and food colouring. Once it has cooled a little, pour over the 18cm/7in cheesecake. Cool in the fridge or freezer.
For the cream soda topping, heat the cream until just boiling then pour it over the chocolate. When melted, stir in the vanilla paste. Once it has cooled a little, pour over the 15cm/6in cheesecake. Cool in the fridge or freezer.
For the Italian meringue, set up a freestanding mixer with the whisk attachment. Add the egg whites and whisk until soft peaks form when the whisk is removed. Meanwhile, heat the sugar and 3 tablespoons water in a pan until it reaches 120C on a sugar thermometer.
As soon as the sugar reaches 120C, slowly drizzle it into the egg whites with the motor running (take care not to pour the syrup onto the beaters as it might splash). When all the syrup is incorporated the mixture should be shiny and smooth. Continue to whisk until the bowl feels cold. Transfer the meringue to a piping bag fitted with a medium plain nozzle.
To assemble, pipe a few dots of meringue onto each cake board. Carefully trim away any excess pastry and remove the cheesecakes from their tins. Place each cheesecake on the corresponding cake board.
Starting with the largest cheesecake, insert 3 drinking straws in a triangle formation about 5cm/2in apart (these will support the weight of the next layer of cheesecake). Carefully trim the straws to the same height as the cheesecake. Repeat the process with the 18cm/7in cheesecake.
Stack the cheesecakes from large to small and pipe the Italian meringue around the edge of each of the bottom 2 cheesecakes and over the top of the smallest one. Decorate the cheesecakes with white chocolate on the top layer, popping candy on the middle and crystallised ginger on the bottom.