“I would like to remind everyone that its "Big Cock" as in "Large Rooster", not like... "cock" cock.”
— The Big Cock
The Big Cock is a character in Eleven Little Roosters. He is the head of the Rooster Corps, the world's leading organisation of assassins, formed after he shared the responsibility for a powerful superweapon, the Hammer of Cock, between the various organisations, to prevent them all from killing each other. He is constantly having to remind his agents that his name is in reference to a large rooster, not an actual cock. In Double Triple Cross, he met his end when Colonel Cockface handed him a pistol, telling him it was one of Annersby's two-way communicators, but as the Big Cock put it to his head, it was a real gun, and he accidentally shot himself in the head. He bled out after the Colonel told him of his real plan.
It's possible that the Big Cock is a reference to the character of Big Boss from the Metal Gear series.