Sarah Jessica Parker will star in and produce “Spinning Into Butter,” an indie adaptation of Rebecca Gilman’s play. Stage director Mark Brokaw is making his feature debut and Norman Twain and Lou Pitt will produce with Parker. Shooting begins Oct. 10 in New York. The movie will be fully financed by Whitsett Hill Films, an arm of a pharmaceuticals company that is bankrolling its first film. Parker will play the dean of students at a New England college who is thrust into the investigation of a racial hate crime. She’s forced to confront her own feelings about race and her administration’s desire to maintain a politically correct posture.