Heat oven to 200C/fan 180C/gas 6. On a lightly floured surface, roll out the pastry to 5mm thickness and use to line a 25cm loose-bottom shallow tart tin. Cover and chill for 15 mins.
Line the pastry case with greaseproof paper and fill with baking beans. Bake for 10-15 mins until dry to touch, but not coloured. Remove the paper and beans and return the pastry case to the oven for a further 3-5 mins until it is just cooked. Reduce the oven to 180C/fan 160C/gas 4.
In a small food processor, blend the ginger with the parsley and 2 tbsp of sunflower oil to a coarse paste. Spread over the base of the tart case. Scatter the crab meat over the ginger paste. Whisk together the eggs and egg yolks with the crème fraîche, then season. Put the tart tin on a baking sheet and pour in the egg mixture. Return the tart to the oven for 30-35 mins or until just set.
Meanwhile, make the dressing. In a small bowl, whisk together the onions, lime juice, chilli, soy sauce, sunflower oil and sugar with 1 tbsp water. Serve the tart warm with a drizzling of dressing.