To make the mashed potato, dice the potatoes, simmer gently in salted water for approx. 20 mins., drain well. Bring the milk and butter to the boil in the same pan. Remove the pan from the heat, add the potatoes, mix using the whisk on a hand mixer until light and fluffy, season. Spread the mashed potato into a greased, oven-proof dish (approx. 3 litres).
Finely slice the leeks, mix with the oil and salt, spread on top of the mashed potato.
Bake for approx. 15 mins. in the top half of an oven preheated to 180°C. Remove the dish from the oven. Using a spoon, make 4 depressions in the leeks. Crack the eggs one after the other into a cup, carefully slide the eggs into the depressions, season, bake for about another 10 mins.