Boil the rice in slightly salted water in a 1:3 (rice:water) ratio. Drain it well and mix with the beaten eggs and crumbled feta cheese.
Knead a dough from 4/5 cup (200 ml) water, the vinegar and flour - if needed, use more flour.
Roll it out into 2 sheets. Lay 1 out along the bottom of an oiled tray and pour the filling on top in an even layer. Place the other sheet on top and sprinkle with the melted butter.
Bake in a moderate 356°F (180 °C) oven until the dough reddens slightly.
You can also bake the bread in a Teflon pan, while turning it over with a wooden spoon in order to bake evenly on both sides.