For halva ice-cream, combine ice-cream and halva in a bowl, fold halva lightly through ice-cream and freeze until firm (2 hours). Makes 1 litre.
Preheat oven to 180C. Process walnuts, sugar and cinnamon until coarsely ground. Layer four sheets of filo brushed with melted butter, spread over one-third of walnut mixture, cut pastry into four widthways, then roll each into a cigar shape. Place on a baking tray lined with baking paper and brush with extra melted butter. Repeat with remaining pastry and nuts and bake until golden (15-25 minutes). Transfer to a heatproof shallow tray and set aside.
For honey syrup, combine ingredients in a saucepan with 60ml water and bring to the boil, stirring to dissolve sugar. Pour over baklava fingers, stand for 5 minutes, and serve warm with halva ice-cream and shaved halva.