This is the prelude to an article published in Sports Illustrated magazine on August 17, 1959:
Lessen, poisoned gulls, ditcher wander hair annulled furry tell a
boarder Slipping Booty? Hoecake? Wail, heresy starry.
As a nonnative English speaker, I don’t quite understand what is going on in the article, but I guess this is some kind of style which uses the same pronunciations of words with different spellings. My question is, what is this technique called? Where and on what purposes is it used?
For a little more context, the preamble to that story in the article you linked says: [Edit: I took this long block out since it was included in cornbread ninja’s answer as well.]
The first line:
Lessen, poisoned gulls, ditcher wander hair annulled furry tell a boarder Slipping Booty? Hoecake? Wail, heresy starry.
can be “translated” (to the best of my ability) as:
Listen, boys and girls, did you want to hear an old fairy tale about a Sleeping Beauty? OK? Well, here’s the story.
The adjective used in the preamble is frammis (a nonsense word you use when you don’t know the real word for what you are describing), but you could describe the technique used to create the story as a stringing together of deliberate mondegreens, or a homophonic transformation. It is not generally used for anything other than amusement.
There is a popular party game here in the US (and elsewhere, I imagine) called Mad Gabs, which utilizes similar constructions.