Heat oven to 200C/180C fan/gas 6. Put all the pastry ingredients except the egg in a food processor. Add a pinch of salt and pulse until it has the consistency of chunky crumbs. Turn the motor back on and crack the egg in. Let it run until the mixture forms a ball, then remove.
Roll the pastry out on a floured surface and use to line 6 x 8cm individual tart tins. Put in the freezer for 5 mins until hard. Line with baking parchment and baking beans. Place on a baking sheet, bake for 15 mins, then remove the parchment and baking beans. Bake for another 5 mins, then remove. Reduce the oven to 160C/140C fan/gas 3.
To make the filling, put the cream in a heatproof bowl and microwave on High for 1 min, or heat over a pan of water. When hot, add the chocolate and stir until melted, then add the vanilla and eggs, whisk well, then pour into the tart cases. Bake for 10 mins, then cool at room temperature.
Meanwhile, make the sugar syrup for the fruit, put the sugar, vanilla pod and 75ml water in a small saucepan. Heat until boiling, then simmer for 5 mins. When it’s syrupy, remove from the heat and add the persimmon. Put back on the heat for 1 min, then remove and cool to room temperature.
Just before serving, add a slice of persimmon and a sprinkle of nuts to each tart.