A “swinger” couple behind a ritzy East Hampton catering business is accused of serving not just food but their own sick appetites by propositioning their workers for sex, a scathing lawsuit claims.

The owner of East Hampton Kitchen, Annie Washburn, and her partner, Michael Castiglione, constantly yapped about their private sex lives, pressured workers to join in the bedroom — and punished people who complained, the suit alleges.

Former catering manager Emma Beudert, who filed the lawsuit in Suffolk County last month, said the “frequent and unwelcome” sexual inquiries and open propositioning of staffers were “disruptive, unlawful and predatory.”

“Ms. Washburn and Mr. Castiglione were extremely inappropriate in the way they discussed and propositioned Ms. Beudert and others about their se

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