Preparing the olives filling:In a medium bowl, press the Kiri square portions with a spatula until the texture becomes smooth and creamy.
Add the chopped olives, the ground thyme, and mix well with a spatula until the filling mixture is homogenous. Set aside.
Assembling the Fatiras:On a floured working surface, and using a rolling pin, spread the puff pastry until it is 1mm thick. Using a round cookie cutter of 12cm in diameter, cut the puff pastry into circles.
Place a full teaspoon of the filling in the center of a puff pastry circle, make sure to leave the edges empty.
In a small bowl, mix the egg yolk and white vinegar, and brush the edges of the puff pastry circle disk.
Put the second puff pastry circle on top, and slightly press the edges to glue the two circles together.
Using a fork, gently press on the edges of the Fatira to decorate it.
Using a knife, gently trace a cross on the surface of the Fatiras then brush them with the remaining egg mixture.
Place the Fatiras on a baking sheet covered with parchment paper.
Bake the Fatiras in a preheated oven at 180C (365F) for 25 minutes until golden brown. Serve warm.