The Pudding Basin is the Fable version of the Bowl Cut. Available in Fable & Fable TLC as a purchasable hairstyle, it is known as the Male Adventurer's Hairstyle in Fable II. It is the default hairstyle in Fable II, and can be purchased after the Hero changes a hairstyle or comes back from the Spire.
There is a quest available in Fable and Fable TLC that is central to this hair style, Beardy Baldy. A man wants to introduce you to his daughter, but says that she,"only looks at men with this hairstyle." He acts rather unintelligent, but as the player walks away he starts snickering to himself, indicating that he is tricking you.