Put butter, sugar and flour in the bowl of a food processor and process until smooth. Add yolk and water, then process until mixture just begins to form a ball. Turn pastry out onto a lightly floured surface, knead until just smooth, then pat into a disc. Enclose in plastic wrap and refrigerate for 15 minutes.
To make frangipane, put butter and sugar in the small bowl of an electric mixer and beat until pale and creamy. Add egg and beat until combined. Add almond meal and plain flour, then beat until just combined. Set aside.
Preheat oven to 180°C. Grease 2 oven trays with butter, then line with baking paper. Roll out pastry on a floured surface until 5mm thick. Cut out 4 rounds using a 7.5cm round pastry or biscuit cutter. Lightly knead pastry scraps together until just smooth, cover and refrigerate while filling first batch.
Lay rounds of pastry on a clean surface and brush with water. Place 1 shallow teaspoon of fig jam in the centre of pastry and spread out a little. Top with 1 teaspoon of the frangipane. Form a triangle casing with the pastry by gently pinching the edges at 3 separate points. Make sure pointed ends are tightly pinched together to avoid opening when baking. Place a mound of flaked almonds on top. Repeat rolling, cutting and filling with remaining pastry, frangipane and almonds.
Put pastries on prepared trays and refrigerate for 15 minutes. Bake for 15-20 minutes or until golden. Leave to stand on trays for 5 minutes before transferring to a wire rack to cool completely. Drizzle with honey to serve.