Peel and finely grate the garlic. Mix with a pinch of salt, then mash into a paste with the flat side of a knife.

In a medium bowl, combine the yogurt, garlic paste, dill, and salt and pepper to taste. Divide the yogurt mixture evenly between two plates and set aside.

Bring the water to a boil in a large pot. Add the vinegar, then reduce the heat to a gentle simmer. Crack each egg into a small cup and slide it carefully into the water. Poach until the white is set; a soft yolk generally takes about 3 minutes. Use pasteurized shell eggs if serving with runny yolks, or cook until both white and yolk are firm. Lift out with a slotted spoon and drain briefly before serving.

In a skillet over medium heat melt the butter. Add a big pinch of salt and the Aleppo pepper or hot paprika.

Divide the eggs between the two plates and drizzle the butter over them. Serve with warm pita that has been cut into quarters.