Heat a griddle pan over a moderate heat until hot.
Construct the sandwiches by arranging the ham and cheese between two slices of the bread. Remove the crusts using a sharp knife. Cook on a griddle pan, turning once coloured and marked on one side. Flip carefully to cook the other side until coloured and marked.
Meanwhile, heat the vegetable oil in a large frying pan over a medium heat. Fry the eggs until set, seasoning at the same time. Arrange the toasted sandwiches on serving plates and top each with a fried egg.
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For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home.
If serving vulnerable groups, elderly people, toddlers, pregnant women and people who are unwell, cook eggs until the whites and yolks are solid.