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1.
Monfay is a replacement word. Its meaning depends on the situation.
Definition 1:
shut the monfay up.

Definition 2:
your so monfay.
by monfayisourword July 18, 2010
 
2.
Your face on Monday morning which is still grimacing from all the crap that you shoveled into it over the weekend, i.e., Jager shots, beer, chicken wangs, chili dogs, boiled okra, dongs, clam sauce.
Yo girl, don't let the boss see your Monfay. If he do, he gon know you was clurbin last night.
by Ronaldo Macadonaldo August 11, 2014