Not a type of cheese, but a cake made to celebrate a birth. 'Cheese' in the sense of being a flattened cylinder in shape.

Known from many local and literary references at least since William Sampson's play 'The Vow Breaker. Or, The Faire Maide of Clifton' of 1630; "bring the groaning cheece, and all requisites, I must supply the fathers place, and bid god-fathers." There is a certain odd tradition of the cake being eaten from the middle outwards until there is a hole big enough to pass the baby through.

Bernard Mandeville's 17th Century version of Aesop's Fables 'writ in familiar verse' has;
Says Ren; pray see what I got here;
It is a groaning Cheese, 'twas made
From Io's Milk, and Faunus had
The ordering of it, 'twould have been
Kept for Dame Juno's Lying in,



Daily Telegraph, 17 Nov 2017