Frances Anne Kemble (1809-1893), Records of Later Life
(New York Henry Holt and Company, 1882), p. 220:
I remember, at a party, being seated by Sydney Smith, when Mrs. Grote entered with a rose-colored turban on her head, at which he suddenly exclaimed, "Now I know the meaning of the word grotesque!"
Another version, the earliest I can find, of this oft-repeated anecdote, from an unsigned article, "English Singing-Birds in Florence," Scribner's Monthly
4.5 (September 1872) 616-620 (at 617):
Of professional jokers, [Charles] Lever was the most obstinate and obstreperous and iterative. Flashes of silence were as rare with him as they were with Macaulay himself. The jokes were always uttered, too, with overwhelming assurance that they could never become stale or flat. There was a pun of Sydney Smith's, and not a very eminent one, which he seemed never to tire of telling. Mrs. Grote, the wife of the distinguished historian, appeared once at a soirée with a queer sort of turban on her accomplished head. "Look at that," said Sydney, "that's the origin of the word grotesque."
Id., p. 616:
In 1855 there was quite a nest of English singing-birds in Florence...
Sydney Smith died in 1845.