A steak and kidney pie is a typical British dish with a filling of diced beef steak and beef kidneys in a thick sauce. It is often, but not always, a one-crust pie, which means that the filling is covered but not completely enclosed by the pastry.

The sauce typically consists of beef broth, flavoured with salt, pepper and parsley, onions, and thickened with flour, cornstarch or beurre manié. Two-crust steak and kidney pies are best made with hot water crust pastry, which is less likely to get soaked in sauce, but one-crust pies may also be made with puff pastry or shortcrust pastry.

Steak and kidney pudding is a similar dish in which the contents are placed into a pudding dish lined and covered with suet pastry. The pudding is then steamed for several hours.

Steak and kidney pudding/pie is sometimes colloquially known as Kate and Sidney pudding/pie or (especially in the British Armed Forces) as a "Baby's Head".

References

The Long Trail: Soldiers Songs and Slang 1914-18 by John Brophy and Eric Partridge ISBN 0722118856