In a small bowl, combine the garlic, yogurt and pinch of salt; mix well.
In a large saucepan or stockpot, combine water, vinegar and 1 teaspoon salt; bring to a boil over high heat. When the water is boiling hard, reduce the heat and gently break the eggs into the water, spacing them well apart. Cook until the whites have set over the yolks, immediately remove the eggs with a slotted spoon and place on a serving dish.
Melt butter in a small skillet or saucepan. Stir in paprika. Pour yogurt sauce over eggs and top with paprika butter. Your cilbir is ready!