Preheat oven to 180°C and line a baking tray with baking paper. Lay one of sheet puff pastry on prepared tray, paint with chutney and sprinkle with walnuts and 1 tbs thyme, leaving a 10cm circle in the middle bare. Top with the second layer of puff pastry.
Cut out a brie-sized circle from the puff pastry layers, then cut diagonal lines outwards at regular intervals approximately 3cm apart, making sure not to cut all the way to the centre. Lift one section up gently and twist 3 times clockwise, then place back down. Lift the next section and repeat twisting motion, but in the opposite direction. Continue around until all sections are twisted.
Place the wheel of brie in the centre hole and brush pastry with egg. Bake for 25 minutes or until pastry is puffed and golden. Sprinkle with remaining thyme and walnuts, serve hot.