To make the mushroom à la greque, add all the ingredients except the chives and mushrooms to a saucepan and simmer for 5mins. Season then add the mushrooms. Simmer for 3mins then remove the pan from the heat. Leave to cool.
For the flatbreads, add all the dry ingredients to a bowl. Pour in the oil then the water. Knead the mix until a dough is formed. Take a small ball and roll out until ¼cm think. Place on the griddle and cook for 1min on each side. Place on a flat.
To poach the eggs, add the vinegar to a large pan of simmering water. Using a spoon create a whirlpool in the water then crack the eggs into it. Poach for 3mins then take out carefully.
To serve, add the chives to the mushrooms, spoon onto the flatbread and top with the poached egg.