Melt the butter in a medium sized saucepan and stir in the flour.
Cook for 2 minutes over moderate heat, then gradually add 10 fluid ounces [1 1/4 cups] of milk, stirring all the time.
Bring slowly to the boil and simmer over low heat for 2-3 minutes, still stirring.
Remove the pan from the heat.
Add the chopped chicken and ham, grated Cheddar and lightly beaten egg yolks.
Mix well and season to taste pepper.
Spread the mixture on to a plate.
Cover and leave to get cold, preferably overnight in a refrigerator.
When cold and set, divide the mixture into 8 equal portions.
Roll into neat sausage shapes.
Beat the whole egg and 2 tablespoons of milk together in a shallow dish.
Dust each croquette with flour, then dip in the beaten egg mixture.
Drain well then coat in breadcrumbs.
Heat a pan of fat to 375 °F (190 °C) and deep fry the croquettes for about 3 minutes.
Drain on absorbent kitchen paper and serve immediately.