The story
Attested as early as 1639 as faire words butter noe parsnips, alluding to the English habit of buttering foods to make them more palatable. It was found in the 17th century in various forms with the first and last word being different, thus allowing combinations of fine/fair/soft with parsnips/cabbage/fish/connie before becoming standardized in the form fine words doth butter no parsnips.
Etymology from Wiktionary, CC BY-SA 4.0.