Masato and I both cite the same broadside, but I suspect that I may have been thinking of a different Green Fields of America from the one Dicho had in mind. Here is the song from Songs of the West referred to above:

BOTH SEXES GIVE EAR TO MY FANCY

(Noted by Sabine Baring Gould and H. Fleetwood Sheppard from John Rickards of Lamerton, Devon)

Both sexes give ear to my fancy,
In praise of sweet woman I sing,
Confined not to Doll, Sue, or Nancy;
The mate of the beggar or king.
When Adam was first a-created,
And lord of the universe crown'd,
His happiness was not completed,
Until that a helpmate was found.

A garden was planted by Nature,
Man could not produce in his life,
But no rest had he till his creator
Discovered he wanted a wife.
He had horses and foxes for hunting
Which most men love dearly as life,
No relishsome food was a wanting
But still... he was short of a wife.

As Adam was resting in slumber,
He lost a small rib from his side,
And when he awoke - 'twas in wonder,
To see a most beautiful bride.
In transport he gazèd upon her,
His happiness now was complete;
He praisèd the bountiful Donor,
Who to him had given a mate.

She was not taken out of his head, sir,
To rule and to triumph in man.
Nor was she took out of his foot, sir,
By him to be trampled upon.
But she was took out of his side, sir,
His equal co-partner to be;
So, united is man with his bride, sir,
Yet man is the top of the tree.

Then let not the fair be despisèd
By man, as she's part of himself.
By woman let man be a-prizèd
As more than the world full of wealth.
A man without woman's a beggar,
Tho' by him the world were possess'd
But a beggar that's got a good woman
With more than the world is he bless'd.

From Songs of the West (Sabine Baring Gould, H. Fleetwood Sheppard and F.W. Bussell; in this case the revised edition of 1905). Baring Gould's full notes are as follows:

"This old song is a favourite with the peasantry throughout England. The words are printed in Bell's Songs of the English Peasantry, p. 231. He says, We have had considerable trouble in procuring a copy of the old song, which used, in former days, to be very popular with aged people resident in the North of England. It has been long out of print, and handed down traditionally. By the kindness of Mr. S. Swindells, printer, Manchester, we have been favoured with an ancient printed copy. "

"In the original the song consists of ten verses. The earliest copy of it that I know is in The Lady's Evening Book of Pleasure, about 1740. It will be found in a collection of garlands made by Mr. J. Bell about 1812, and called by him The Eleemosynary Emporium. It is in the British Museum. The air is found in Vocal Music, or the Songster's Companion, 2nd ed., 1772, to the song, Farewell You Green Fields and Sweet Groves, p.92. It was taken into The Tragedy of Tragedies, or Tom Thumb, 1734, as the air to In Hurry, Post-haste for a licence, and was attributed to Dr. Arne. In Die Familie Mendelssohn, vol.ii., is a scrap of music written down by Felix Mendelssohn, dated Leipzig, 16th August 1840, which is identical with the first few bars of this melody. But the earliest form of the air is in J.S. Bach's Comic Cantata, where a peasant sings it."

"We took the song down from John Rickards, Lamerton, and again from J. Benney, Menheniot. Mr. Kidson prints a Yorkshire version in his Traditional Tunes, 1891. Miss L. Broadwood has noted it down from the singing of a baker at Cuckfield, Sussex. Dr. Barrett gives our melody to The Gallant Hussar, No. 13 [in S.O.W]. We have also taken it down to this ballad; so has Mr. Sharp in Somerset."

A midi of the tune as given in Songs of the West can be heard, until it becomes available at Mudcat Midis, via this link:

Both Sexes Give Ear (midi)

Other versions of this song have been found in various parts of England, often as Old Adam or When Adam Was First Created; under the latter title it remains in the repertoire of the Copper family of Rottingdean, Sussex. There are several examples from Aberdeenshire in the Greig-Duncan collection, and the song was also quite widespread in the USA and Canada. There is a rather different example in the DT:

WEDLOCK  from White Spirituals of the Southern Uplands.

Roud Folk Song Index number 728.

There are broadside copies under a number of titles at Bodleian Library Broadside Ballads:

When Adam was first created ("Both sexes give here [sic] to my fancy ...")  Printed between 1840 and 1866 by J. Harkness, Church-Street, Preston. [Largely illegible] 2806 c.13(192)

Adam & Eve ("Both sexes give ear to my fancy ...")  Printed by Wm. Ford, York-st. Sheffield [no date]. Firth b.25(242)

In praise of dear women I sing ("Both sexes give ear to my fancy ...")  Printed by Liptrot, St. Helen's [no date]. Harding B 28(19) and Harding B 28(175)

Old Adam ("Both sexes give ear to my song ...")  Printed c.1837 by J. Wheeler, Manchester. 2806 c.17(319)