For the rough puff pastry, place the flour and salt into a large mixing bowl. Add the butter and use your hands to rub the butter into the flour.
When the flour and butter mixture resembles breadcrumbs, add the cold water. Mix it in with a palette knife to keep the mixture cool. When the mixture comes together to form a dough, turn it out onto a clean, floured surface and knead briefly until just smooth.
Form the dough into a rectangular block (this will make it easier to roll out later), wrap in cling film and refrigerate for 20 minutes.
Roll the chilled dough out onto a clean, floured surface into a rectangle about 40x20cm/16inx8in. Fold one-third of the dough into the centre, then fold the other third over that.
Give the pastry a quarter turn and repeat step 4.
Wrap the pastry block in cling film, refrigerate for 20 minutes then repeat steps 4 and 5.
Wrap the pastry block in cling film and refrigerate for 30 minutes before using.
Meanwhile, for the pear tatin, preheat the oven to 200C/400F/Gas 6.
Place the pears, 25g/1oz of the sugar and all of the lemon zest and vanilla seeds into a saucepan. Fill the saucepan with enough water to just cover the pears. Heat the pears over a gentle heat until the mixture is simmering. Simmer for 15 minutes, or until the pears are just tender. Drain the pears and pat dry.
Heat the remaining 85g/3oz of sugar in a 24cm/9Â½in ovenproof frying pan over a low heat until is has caramelised. Add the butter, cream, star anise and cinnamon to the pan and heat gently until the mixture forms a smooth caramel. Discard the star anise.
Place the pears into the caramel, cut-side up.
Roll the chilled pastry out onto a floured surface to a 0.5cm/Â¼in thickness. Cut the pastry into a circle slightly larger than the frying pan.
Place the pastry circle over the pears, tucking the edges of the pastry inside the pan to surround the pears.
Transfer to the oven to bake for 20-25 minutes, or until the pastry is risen and golden-brown and cooked through. Once cooked, remove the pear tatin from the oven and set aside to cool for 5-10 minutes.
To serve, invert the tarte tatin onto a serving plate. Slice the tatin into wedges and place a slice onto each of 4 serving plates. Top each slice with a scoop of vanilla ice cream.