Green’s Dictionary of Slang

(Aus.) to eat (greedily).

1771		R. King New London Spy 51: [M]unging something out of a wooden bowl, and muttering the whole time he was eating.
2005		L. Redhead Rubdown [ebook] I stuffed salty fries in my mouth [...] I was so intent on munging down my junk, food that I didn’t hear the footsteps behind me.