In a large bowl, mix together the flour, water and salt.
Mix until getting an smooth dough. Knead and set aside.
In a saucepan boil the potatoes with water an a pinch of salt, until tender.
Sauté the onions in a frying pan with a little of butter.
Mash the potatoes and add some of the onions.
Roll out the dough on a cutting board. Cut out of the dough circles from around 10 cm diameter (or enough for fitting in the palm of your hand).
Put a spoon of the potato mixture in the center of the circle. Seal the sides together (getting half moon shapes).
Drop each Vereniki into boiling water for 7 to 10 minutes or until they float.
Drain them off and serve with the rest of the onions and some melted butter.