For the jam, place the strawberries in a small pan with the sugar and cook over a low heat until the sugar has melted. Add the knob of butter. Bring to the boil and boil vigorously for four minutes, or until the temperature on a sugar thermometer reaches 104C/219F (setting point). Remove from the heat and stir in the knob of butter. Transfer to a large bowl and leave to set.
For the sponge rolls, preheat the oven to 220C/fan 200C/425F/Gas 7. Grease and line two 33cm x 23cm/13 x 9in Swiss roll tins with baking parchment. Whisk the eggs and sugar together in a large bowl until the mixture is light and frothy and the whisk leaves a trail when lifted out. Sift the flour into the mixture and carefully fold it in. Divide the mixture between the prepared tins and give it a gentle shake so that the mixture finds its own level, making sure that it has spread evenly to the corners.
Bake in the two Swiss roll tins for 10–12 minutes, or until the sponges are golden-brown and begin to shrink from the edges of the tin. While the cakes are cooking, place two pieces of baking parchment a little bigger than the size of the tin on the work surface and sprinkle with caster sugar.
Turn the cakes out onto the sugared parchment and peel off the paper. Trim the edges of the sponges with a sharp knife and score 2cm/¾in from the short edge, being careful not to cut right through.
Leave to cool slightly, then spread with jam and roll up the cakes firmly from the scored end and set aside.
For the bavarois, soak the gelatine in cold water until soft. Purée 450g/1lb of the raspberries in the bowl of a food processor. Pass the raspberries through a sieve over a bowl and discard the seeds. Stir the raspberry liqueur into the purée and set aside.
Pour the milk into a pan and heat until just under boiling point. Whisk the egg yolks and caster sugar together until pale and creamy. Pour the hot milk over the eggs and whisk together. Drain the gelatine, squeezing out any excess moisture and add it to the custard. Return the custard to the pan and cook until the mixture coats the back of a spoon. Do not boil as this will split the custard and prevent the gelatine from setting. Remove from the heat, transfer to a clean bowl and leave to cool slightly before folding in the raspberry purée. Leave to cool for at least 30 minutes.
Meanwhile, line the base of a 2 litre/3½ pint round bowl with cling film, to help turn the Charlotte royale out. Slice the Swiss rolls into 1.5cm/⅝in slices and use to line the base and sides of a bowl. Pack the slices closely together so that no filling can seep through, reserving enough slices to cover the top (which will become the base).
In a bowl, whip the cream until soft peaks form when the whisk is removed from the bowl and stir into the raspberry bavarois. Fold in the remaining 100g/3½oz of raspberries and the small strawberries and spoon into the lined bowl.
Cover with the remaining cake slices. Cover with cling film and chill in the fridge overnight until set.
Turn out the Charlotte royale onto a cooling rack.
To decorate, tip the caster sugar into a pan with 125ml/4fl oz water and bring to the boil. Dissolve the arrowroot in two tablespoons of cold water and stir into the sugar syrup. Bring to the boil, remove from the heat and leave to cool slightly before spooning over the Charlotte royale to glaze.
Whip the cream and icing sugar in a bowl until soft peaks form when the whisk is removed from the bowl and spoon into a piping bag fitted with a medium star nozzle.
Pipe a continual scallop design of cream around the base of the Charlotte royale and decorate with fanned and glazed strawberries.