Mix the beef with the potatoes, salt and pepper to taste and enough milk to make a soft consistency.
Form the mixture into four rounds and hollow out the centres.
Melt the butter in a frying-pan.
Add the beef and potato rounds and fry for 5 minutes or until the rounds are evenly browned.
Spoon a little of the hot fat into the centres and break an egg into each hollow.
Continue cooking for a few minutes or until the egg whites have set.
Lift out carefully and garnish with the tomato slices.