Roll out the puff pastry thinly, place onto baking parchment and rest in the fridge for 10 minutes. Cut the goat cheese into 4 even ½ inch thick pieces. Cut 8 circles out of the pastry. Place 4 circles onto a non-stick baking tray with a slice of goat cheese in the middle and a dessertspoon of fig relish on top of each.
Crack the egg into a bowl and whisk well with a pinch of salt, then brush around the edge of the pastry circles. Place a second circle of puff pastry on top and carefully seal around the edges. Score crossing lines in the top and brush with the egg wash. Place into the fridge for 15 minutes to rest. Bake for 12 minutes. Serve straightaway.