Green’s Dictionary of Slang

(Ulster) the tongue; usu. in phrs. break one’s melt, to infuriate one beyond reason; keep in your melt, hold your tongue; knock in one’s melt, to drive one mad.

1950		S. Murphy Stone Mad (1966) 135: Many’s the pound I’ve earned for him an’ I’m not going to break me melt at this hour of the day.
1997		Share Slanguage.
2015		L. McInerney Glorious Heresies 93: ‘Oh my God, you break my melt, d’you know that?’.