Using a food processor, cut the butter into the flour, icing sugar and salt, then incorporate the water and vinegar by hand just until you have a smooth dough. Roll into a ball, wrap it in plastic wrap and refrigerate for 1 hour.
Shaping and Blind Baking
Preheat the oven to 180°C (350°F/Gas 4). If the pastry dough is too hard when it comes out of the refrigerator, let it soften. Butter and flour a 26 cm (10½ inch) pie dish. On a floured surface, roll out the dough into a round large enough to hang over the edge of the dish by about 3 cm (1¼ inches). Place the round of dough in the dish, then roll the overhang onto itself and pinch with your fingers to shape the edge. Prick the pastry base with a fork, cover with baking paper and dried beans and bake for 15 minutes. Remove the paper and beans and brush the base with the beaten egg. Return to the oven for 2 minutes until dry and light golden, lowering the temperature to 170°C (325°F/Gas 3).
Combine the polenta, vinegar, vanilla, eggs, cream and salt. In a pan, bring the butter, sugar, sugar syrup and honey to the boil. Lower the heat and stir in the egg mixture, mixing with a spatula for about 5 minutes until you have a smooth cream. Do not boil.
Assembly and Cooking
Preheat the oven to 180°C (350°F/Gas 4). Pour the filling into the precooked pie shell. Bake for about 40 minutes until the filling is set, but still a little wobbly. Allow to cool and sprinkle with the fine sea salt.