To make shortcrust pastry, place flour and butter in a food processor. Process until fine crumbs form. Add egg yolks and water. Process until dough just comes together. Turn onto a lightly floured surface and gently knead until smooth. Shape into a disc. Wrap in plastic wrap. Place in fridge for 30 mins to rest.
Preheat oven to 200°C. Roll out the pastry onto a lightly floured surface to a 3mm-thick disc. Line six 8cm round tart tins, with removable bases, with pastry. Use a sharp knife to trim excess. Place in fridge for 15 mins to rest.
Line pastry with baking paper and fill with pastry weights or rice. Place on a baking tray. Bake for 10 mins. Remove paper and weights or rice. Bake for 8-10 mins or until light golden. Remove from oven. Reduce oven to 160°C.
Meanwhile, melt the butter in a frying pan over low heat. Cook onion, stirring, for 5 mins or until onion softens. Add the garlic and half the thyme. Cook for 1 min or until aromatic. Add combined mushroom and cook, stirring, for 5 mins or until mushroom is tender. Cool slightly.
Whisk egg and cream in a jug. Season. Divide mushroom mixture and goat’s cheese among pastry cases. Top with egg mixture and remaining thyme. Bake for 20 mins or until just set.