Preheat oven to 200°C and heat a large baking tray inside.
Pulse flour, butter, and salt in a processor until the mixture looks like breadcrumbs.
Mix in one beaten egg and 15ml of water to form a dough ball.
Roll out dough on a floured surface to 3mm thickness.
Press chopped walnuts into the pastry using cling film and a rolling pin.
Cut eight circles to line the Yorkshire pudding tins and chill in the fridge.
Cook shallots in oil over high heat for 2 minutes, then cover and soften for 10 minutes.
Add vinegar and sugar, then caramelise for 15 minutes before cooling.
Mix goats' cheese, two beaten eggs, and half the parsley until smooth.
Prick tart bases, spoon in shallots, and pour cheese mixture on top.
Bake on the hot tray for 20 minutes until crisp and golden.
Sprinkle with remaining parsley and serve.