Jonathan Demme.

Jonathan Demme got his start directing Caged Heat (1974), everyone's favorite women-in-prison film. Yes, that's a real genre, women-in-prison, and Caged Heat is the women-in-prisoniest of them all. The movie has "boobs and blood aplenty," yet also features strong female leads.

Hmm. Blood + boobs + strong female lead = the perfect combination to direct The Silence of the Lambs, a film about a man who kidnaps and skins women and the female FBI agent pursuing him. The Silence of the Lambs made Demme a household name and earned him an Academy Award for Best Director. But Demme didn't forget his roots. Roger Corman, who gave Demme his first directed role on Caged Heat, cameos as the FBI director in Lambs. (Source)

Demme had previously directed Married to the Mob (1988) starring Michelle Pfeiffer, and wanted Pfeiffer to star as Starling in Silence, but she didn't want to be in a film so violent (source). So the studio selected Foster, who soon impressed Demme with her presence and her accent.

Demme, Hopkins, Foster, and screenwriter Ted Tally made the perfect team. You'd think they'd all be back for the sequel, Hannibal, almost a decade later. But Demme read the novel and was "horrified," not in a good way. He passed on that project, which was picked up by Ridley Scott (Alien, Blade Runner).

Since then, Demme has directed many other films, but only one featuring a sadistic sociopath who just might be a cannibalistic serial killer: Rachel Getting Married (2008) starring Anne Hathaway.