h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Can't say for certain when the first Egg Banjo was made and served, but one could speculate that it had to follow the invention of the Banjo itself.

However, that isn't necessarily so. I found this on an online etymological site:

[banjo
1764, Amer.Eng., usually described as of African origin, prob. akin to Bantu mbanza, an instrument resembling a banjo. The word has been infl. by colloquial pronunciation of bandore (1566), a 16c. stringed instrument like a lute and an ancestor (musically and linguistically) of mandolin; from Port. bandurra, from L. pandura, from Gk. pandoura "three-stringed instrument." The origin and influence may be the reverse of what is here described.]

Now, the Mandoline is a device for slicing food, and they are sometimes referred to as banjos because of the banjo strumming action with which the hand guides the food across the blade.

One more theory for the pot!

That's the most convincing etymology for banjo I've seen. There are string instruments with similar names in many languages: bandoura or bandura in the Ukraine, bandurria and bandola in Spain and Latin America, and the mandolin is called bandolin in Spanish and bandolion in Portuguese. Curiously, though etymological dictionaries like the word 'bandore' for the 16th century instrument, Grove (the musician's reference book) gives its name as bandora or pandora, with pandore and bandore as the French translation and bandoer as the German.

The first printed English solo songs (it says here in Grove) had bandora accompaniment. It was a member of the theatrical consort, with deep buzzy brass strings.

The bandora was one of the things
That Shakespeare employed in the wings
Deep, sweet-voiced and gentle
Its great sentimental
Appeal helped him pull the heart-strings

Just !

Only thing that still concerns me is an apparently possible military connection.

Understandable that a soldier should cobble together a stringed instrument out of an old drum head . . .

Put a neck and some strings on a drum
And your banjo is ready to strum
With a pick, or a couple
Or if you are supple
Try using two fingers and thumb

Claw hand! That's my style!

"Banjo", as a verb, was also current British army slang in the 1980's, and possibly lives on today, as a verb denoting to "beat up", "to batter senseless", "to engage in a winning fight with".

A preventative to liquid yolk flying everywhere except into the mouth is of course to open the sandwich and batter the yolk into the bread - ie, deliberately break it, and allow the bread to soak it up. (effectively, to banjo the yolk).

A consideration to be taken into account if in uniform, and aware that people who wear stripes are quite capable of chastising a conspicuously messy eater who gets egg yolk on the Queen's uniform...

Could the verb banjo arise from banjax?

OED entry for banjax (v):

Anglo-Ir. slang.
[Etym. unknown; perh. orig. Dublin slang.]

trans. To batter or destroy (a person or thing); to ruin; to confound, stymie. So banjaxed ppl. a., ruined, stymied.

1939 ‘F. O'BRIEN’ At Swim-two-Birds 240 Here is his black heart sitting there as large as life in the middle of the pulp of his banjaxed corpse. 1956 S. BECKETT Waiting for Godot (rev. ed.) 79 Lucky might get going all of a sudden. Then we'd be banjaxed [1954: ballocksed]. 1959 D. O'NEILL Life has no Price ix. 169, I had the right to leave him talk, I suppose, and banjax us altogether? 1968 Observer 29 Dec. 19/1 You completely banjax the whole psychological impact. 1969 G. LYALL Venus with Pistol viii. 48 The man is a twit. I mean, he banjaxed that Zurich trip. 1972 New Yorker 28 Oct. 40/1 Ha-ha, so she ups and banjaxed the old man one night with a broken spade handle. 1974 Nature 22 Nov. 334/1 My sense of enlightenment was somewhat tempered by the banjaxed mood in which I found myself. 1976 U. HOLDEN String Horses viii. 102 The dawn suicide the day before had made a lot of work and worry, had banjaxed things for a while. 1979 T. WOGAN Banjaxed (1980) 78, I am out to banjax the bookies.

A fried egg banjo,indeed any fried sandwich is called a banjo because a frying pan is called a banjo because of its shape

Intriguing! But why is it limited to sandwiches then? Do you banjo your breakfast?