In a crossword puzzle, the clue is “Yolk surrounder” and the answer is “whittle.” I’ve never heard of this before (and I’ve been around a while :)) and all I’ve found on Google is reference to the crossword. It’s tempting to think the puzzle-maker just made it up.
Has anyone ever run across the word “whittle” meaning the white of an egg?
I have the full 20-volume Oxford English Dictionary in my office, which contains just about every obscure word and usage ever, and there is no mention of whittle meaning egg-white.
I think the crossword compiler misfiled his clue for WHITE. 
It’s part of the puzzle theme for this particular puzzle - letters are removed or inserted from some words before they’re entered into the grid. In this case, the solution to “yolk surrounder” is indeed WHITE, but the TL is added to make WHITTLE.
If you want a fuller explanation of how that particular puzzle works, read this blog post. It’s from the Wordplay blog on the New York Times website. The blog discusses each daily puzzle and offers hints on how to solve it.
:smack: I was aware of the theme, but somehow failed to notice that this particular clue was for one of those “add two letters” words.
Looking at the OED online I see that “whittle” is an obsolete noun meaning mantle or cloak. By stretching a point one could conceivably say the egg-white is a mantle of sorts, but none of the quotations listed backs that up.
Fifty five year old Australian here and I’m familiar with the term, it’s not something I’d say but very surprised its not in the dictionary.
AFAIK Whittle is what you do with a sharp knife to turn a scrap piece of wood into shavings.
As a verb, yes, but this clue calls for a noun. As mentioned above, the answer is “white” (short for “the white of an egg”), with “tl” inserted per the theme of the puzzle. The resultant word only needs to be a legitimate word (not necessarily a noun), so “whittle” is the entry. I was confused because I overlooked the modification called for by the theme, and thought they were saying “whittle” was a noun that meant egg white.