Preheat the oven to 180C/360F/Gas 4.
For the baklava, brush a 25cm/10in x 18cm/7in baking tray with some of the melted butter.
Trim the filo pastry to fit the baking tray if necessary.
Place one of the filo sheets into the tray. Brush with butter then place another filo sheet on top and brush with butter. Repeat to use up half of the filo sheets in this way.
Meanwhile, mix the walnuts and pistachio nuts together thoroughly in a bowl.
Pour the nut mixture onto the buttered filo pastry stack and spread out evenly.
Brush one sheet of filo with butter then place it, butter-side down onto the layer of nuts. Brush the sheet with butter, then repeat the layering process with the remaining filo sheets, again buttering each sheet before adding the next.
Using a large sharp knife, score the top of the layered stack in a diamond pattern.
Place into the oven and bake for 20-25 minutes, until golden and cooked through.
Meanwhile, place the caster sugar, water, lemon juice and ground ginger into a pan over a medium heat and bring to the boil. Boil for 5-6 minutes, until just thickened to a syrup.
When the baklava comes out of the oven, pour the warm syrup over and set aside to cool.
For the ice cream, place the cream, ginger syrup, ground ginger and honey into a freezer-safe bowl and whisk until soft peaks are formed when the whisk is removed.
Add the chopped almonds and ginger and fold together gently.
Place into the freezer for two to four hours, or until set solid. Remove the ice cream from the freezer ten minutes before serving.
To serve, separate the baklava diamonds and place two onto each plate. Top with a scoop of ice cream and serve.