Bring a saucepan of water with a splash of vinegar to the boil.
Meanwhile, mix your yoghurt with the garlic, mint, paprika and salt and divide between two plates.
Swirl a spoon in the centre of the yoghurt to spread it out and leave a well in the centre.
Crack your eggs one at a time onto a small plate, taking care not to break the yolk.
Stir your boiling water with a whisk so that it starts to swirl.
Whilst the water is swirling, carefully pour one egg into the centre of the swirl and poach for 2-3 minutes.
Remove the egg with a slotted spoon and place into the iced water. repeat the process for the remaining three eggs.
Leave the boiling water on the heat.
If you are having your çılbır with toasted bread, start to toast it now.
Meanwhile, gently heat your butter and chilli flakes over a low heat and stir until the chilli has infused and the butter is starting to bubble. Remove from the heat.
Now place all four poached eggs back into the simmering water for 30 seconds to reheat. The eggs can all go into the water together.
Remove each one carefully with a slotted spoon and drain before placing two eggs into the centre of each yoghurt well on your plates.
Drizzle the melted chill butter over the poached eggs and yoghurt and serve immediately with your hot, toasted bread.