Green’s Dictionary of Slang

1. the gold braid that adorns a senior officer’s cap.

1940		Phila. Eve. Ledger 20 July n.p.: ‘Scrambled eggs’—brass decorations on the cap visors of officers ranking as majors or better.
1944		H. Hunt East of Farewell 130: The gold leaves on his visor shone in the morning sun [...] ‘I see you’re wearing your scrambled eggs,’ the Old Man said.
1967		(con. 1940s) M. Dibner Admiral (1968) 267: His father’s newly won commander’s cap bright with its ‘scrambled eggs’ on the black visor.
2002		P. Fussell Uniforms 59: But the full-dress generals’ cap is the prizewinner in the vulgarity sweepstakes: showy gold bullion ‘scrambled eggs’ on both visor and crown.

2. a senior officer.

1943

C.H. Ward-Jackson It’s Piece of Cake 52: Scrambled egg [...] an officer of the rank of Group Captain or above.