Heat the oven to 200C/180C fan/gas 6. Lightly dust a surface with flour, then roll out the pastry to a 45cm long, 4-5cm wide rectangle. Mix the cinnamon and icing sugar together, then sprinkle over the pastry. Roll it up tightly into a fat coil from the short end (it should look like a large cinnamon bun). Dust lightly with extra icing sugar and roll out to a 33cm circle (the cinnamon will be rippled through the pastry and separate a little, but keep rolling, dusting with icing sugar as you go). Line a 22-23cm springform cake tin with the pastry so it comes just over the top of the tin. Prick the base all over with a fork. Line with baking parchment, fill with baking beans and bake for 25 mins. Remove the parchment and beans, brush with the egg white, then bake for 10-15 mins.
Meanwhile, to make the filling put the milk, cream, lemon zest, cinnamon and vanilla in a pan. Bring to a simmer, then remove from the heat and leave to infuse for 15 mins. Strain. Discard the lemon zest and cinnamon stick.
Whisk the egg yolks and flour in a bowl until you have a smooth paste. Slowly whisk in the cream mixture, then return to the pan. Warm over a medium heat, stirring continuously until thick. Transfer to a large bowl.
Heat the oven to 180C/160C fan/gas 4. Put the caster sugar in a pan with 185ml water. Bring to a simmer and leave on a low heat until the sugar has dissolved, then bring to the boil and cook until it reaches 112C on a sugar thermometer. Carefully whisk the syrup into the warm custard, along with a pinch of salt.
Pour the custard into the baked pastry case, and bake in the centre of the oven for 35-40 mins, or until set with a slight wobble in the centre. Heat the grill to high, then grill for 2-3 mins until blackened and blistered on top – cover the edges with foil if needed. Leave to cool completely in the tin. Serve with crème fraîche or soured cream.