For caramel sauce:
Place cream in small saucepan. Scrape in seeds from vanilla bean; add bean. Bring just to simmer. Mix in butter and sea salt; set vanilla cream aside.

Stir sugar, 1/3 cup water, and corn syrup in heavy medium saucepan over medium heat until sugar dissolves. Increase heat; boil without stirring until syrup turns deep amber, brushing down sides with wet pastry brush and swirling pan occasionally, about 12 minutes. Remove from heat. Whisk in vanilla cream (mixture will bubble). Set sauce aside.

For pie:
Preheat oven to 375°F. Line 9-inch-diameter pie dish with foil. Finely grind graham crackers and brown sugar in processor. Add butter and vanilla; blend until moist crumbs form. Add nuts; blend just until finely chopped. Using plastic wrap as aid, press crumbs firmly onto bottom and up sides of foil-lined pie dish. Freeze 15 minutes.

Bake crust until brown, about 15 minutes. Freeze 1 hour. Using foil, lift crust from dish; carefully peel off foil. Return crust to pie dish. Drizzle 1/2 cup caramel sauce over bottom of crust. Freeze 30 minutes. Spoon 1 1/2 pints ice cream into crust; smooth top. Drizzle 3 tablespoons peanut butter over, then 2 tablespoons sauce. Sprinkle with 1/2 cup brittle. Freeze 1 hour. Spoon remaining 1 1/2 pints ice cream over; smooth top. Drizzle 2 tablespoons peanut butter over, then 2 tablespoons sauce. Sprinkle edge of pie with 1/2 cup brittle. Freeze 4 hours. DO AHEAD: Pie can be made 3 days ahead; tent with foil and freeze. Cover and chill remaining sauce.

Cut pie into wedges. Rewarm sauce and pass separately.