To suffer the consequences of one's own actions

I'm tired of her idle complaining and meaningless grudges. As far as I'm concerned, from now on she can steam in her own juice

Non ne posso più del suo continuo lamentarsi e dei suoi bronci ingiustificati. Per quanto mi riguarda, d'ora in poi può bollire nel suo brodo

After my big argument with Steven, my mother said to leave him alone for a while, let him steam in his own juice, he'll get over it

Dopo una feroce litigata con Stefano, mia madre mi ha consigliato di lasciarlo perdere e di lasciarlo bollire nel suo brodo per un po', che gli sarebbe passata

This expression is very old, and its variant "to fry in one's own grease" appears in a 13th-century tale of Richard the Lion-Hearted. It looks like the latter was originally literal, talking about people burning at the stake, having committed crimes punishable by such means