A sex-obsessed Long Island teacher used her position as a department chairwoman to harass male underlings with crude come-ons, unwanted caresses and ribald tales of her wanton past, according to complaints filed with the state Monday.

Cecilia Sanossian, 51, a married mother of two from Garden City, openly referred to the men working under her as “FILFs” — “fathers I’d like to f- -k” — and called one a “hot-fudge chocolate that students want to eat,” the teachers allege in documents obtained by The Post.

She told one male instructor that “she likes to have sex more than her husband,” invited him to come to her house for a shower and smacked her rear end while bragging, “Not bad for a mom!,” the papers say.

“I give the best head,” Sanossian allegedly told another male teacher at Valley Stream North High School and discussed her preference in lingerie, noting she and her sisters were known for their “great asses, but not their breasts,” the complaints say.

She also revealed how she broke a rib during an especially vigorous romp and once woke up next to a naked woman, the papers state.

Two teachers — Al Daddino, 38, of Garden City, and John Brennan, 42, of Brooklyn — plan to file formal complaints against the Valley Stream Central High School District with the state Division of Human Rights, saying they have complained to higher-ups to no avail.

Daddino, who is married, says in his complaint that he suffered such “extreme stress and anxiety” that he started seeing a shrink.

Brennan, who also is married, told The Post his breaking point came when Sanossian said, “You need a back massage,” and began rubbing his shoulders while he was sick with a sinus infection.

“I could feel myself shrinking,” he said. “Then I began to feel powerless. Then I began to understand how people feel who are dealing with sexual harassment.”

Exhibit A in the men’s complaints is a letter they and eight other instructors in their department sent to the school’s principal in May.

“Not all members of the social studies department have experienced these actions, however, those who have not directly experienced these actions, have witnessed these actions,” the letter says.

The men’s lawyer, Lenard Leeds, called it “an unusual case, in that you don’t normally get 10 people corroborating the allegations.’’

Sanossian declined to comment.

Additional reporting by Reuven Fenton and Kevin Sheehan