Robert Waltz wrote:

The Ballad Index, at least, has only seven songs which
I keyed as bawdy and with food references, and none of them about
vegetables. I certainly wouldn't have thought of "Houses in Between"
as a candidate, but I have no alternative to offer.

How about "The Marrow Song" ?

The Marrow Song

There's a man lives down in the street I'd like you all to know
He grew a great big marrow for the local farmer's show
When the story got around, they came from far and wide
When they saw the size of it, all the ladies cried

[Chorus]
Oh, what a beauty, I've never seen one as big as that before
Oh, what a beauty, It must be two foot long or even more
Such a lovely colour, so nice and round and fat
I never thought a marrow could grow as big as that
Oh, what a beauty, I've never seen one as big as that before

[Verse 2]
He was leaning on his garden gate the other day
He beckoned to a lady who lived just across the way
He took her down the garden path and showed her it with pride
When she saw the size of it that little lady cried

[Chorus]
Oh, what a beauty, I've never seen one as big as that before
Oh, what a beauty, It must be two foot long or even more
Such a lovely colour, so nice and round and fat
I never thought a marrow could grow as big as that
Oh, what a beauty, I've never seen one as big as that before

If the version was done by an American singer, the singer would have
"translated" the British "marrow" (cucumber?) into a turnip or other
vegetable.