Egg in beer refers to the practice, literally or figuratively of cracking a raw egg into a glass of beer. One Pennsylvania source refers to this as a "miner's breakfast". In 1915, industry journal The Mixer and Server noted a Seattle case where a judge decreed that an egg, once cracked into a glass of beer, qualified as a drink and was not in violation of ordinances against giving free food in bars.
The term is also used metaphorically, commonly as "what do you want, egg in your beer?", implying that the listener already has something good but is asking for undeservedly more.
References
Egg in beer Wikipedia(Text) CC BY-SA