According to the Oxford English Dictionary (OED – 3rd edition, 2002), easy-peasy originated in British English; the earliest instance that the OED has recorded is from The Bookseller (London) of Saturday 22nd January 1966. But the earliest occurrence that I have found seems to invalidate that origin.
Why do they say Easy peasy?
"Easy-peasy" probably originated in a children's schoolyard chanting game, played e.g. when skipping over a rope, or to choose someone for a forfeit or to be chased. Chants often use nonsense words to achieve a rhyme and are frequently reduplicative like 'easy-peasy'.
Is Easy peasy slang?
Easy-peasy is one of our more recent reduplicatives, dating from the mid-20th century. The word is primarily found in British use (and is often seen in the company of “lemon-squeezy”), recorded in the UK from the 1960s, frequently in children's slang (yes, children can have slang).