Put the flour and butter in a food processor and pulse until the mixture resembles fine breadcrumbs. Add the sugar, pulse again, then add the egg yolk and water. Process until the mixture comes together to form a dough. Wrap in clingfilm and chill in the fridge for 30 minutes.
Preheat the oven to 190°C/gas mark 5. Roll the pastry out on a floured surface and line a deep 21cm loose-bottomed fluted tart tin. Trim the edges and prick all over with a fork. Line the pastry base with baking paper and fill with baking beans. Blind bake for 15 minutes, then remove the beans and paper. Cook for a further 5-10 minutes until golden and dry on top.
Meanwhile, heat the cream, milk and vanilla pod in a pan set over a low heat, until it's just about to boil. Remove from the heat and discard the vanilla pod. Whisk together the sugar and egg yolks in a large heatproof bowl, then slowly pour it over the warm cream mixture, whisking continuously until you have a smooth, thick custard. Stir through the ginger and ginger syrup.
Turn the oven temperature down to 150°C/gas mark 2. While the pastry case is still in the oven, carefully pour in the custard, making sure it doesn't spill over the sides. Bake for 40 minutes or until set. Allow to cool completely in the tin, then carefully transfer to a serving plate. Dust the top with icing sugar to serve.