Poach the eggs lightly until the whites are just set, about 6 minutes. Immediately plunge them into cold water to prevent any further cooking.
Place the beef in a mixing bowl and mix in the curry paste, garlic, mint and some salt. Spread half the mixture into a 15cm cake tin – not one with a loose base -pressing it level with a wooden spoon. Then make four equally spaced depressions with a large metal spoon and place a poached egg into each. Cover with the remaining beef and pat level. Brush the top with a little oil.
Preheat the oven to 240°C/Gas mark 9. Place the beef cake on a high shelf in the oven for 15–20 minutes, or until a darkish brown. Do not cook for any longer than 20 minutes, otherwise the egg will no longer be runny. Remove from the oven and carefully pour the juices out of the tin into a small saucepan. Boil the juices fiercely over a high heat for 2–4 minutes until reduced and syrupy. Carefully turn the cake out of the tin and place onto a serving plate. Spoon the reduced juices over the cake to glaze and serve immediately, cut into slices like a conventional cake.