Place the eggs into a saucepan in a single layer and cover the eggs with water by 2.5cm. Cover the saucepan and bring the water to the boil. Remove from the heat and let the eggs stand in the hot water for 15 minutes; drain. Cool the eggs under cold running water in the sink. Peel and chop the eggs.
Pour the buttermilk into a large bowl; add the eggs, beetroot, cucumber, chives and dill. Stir gently to combine. Chill in refrigerator for 1 full day before serving.