In a medium bowl, combine graham cracker crumbs, sugar, and melted butter. Press into the bottom and up the sides of a 9-inch pie pan. Chill the crust until firm.

Meanwhile, make the filling: Melt butter in a medium saucepan. Stir in brown sugar and cook and stir over medium-low heat until dissolved. Add the sweetened condensed milk and bring the mixture to a boil for a few minutes. stirring constantly until the filling becomes thick and darkens. Remove from heat and stir in vanilla.

Layer the sliced bananas in the crust. Pour the toffee filling over the bananas. Refrigerate for at least 2-3 hours, or until firm.

When ready to serve, beat the cream and sugar with an electric mixer on high speed until stiff peaks form. Spread whipped cream over chilled pie and top with chocolate shavings.