In a saucepan over medium-low heat, stir together brown sugar and butter until butter melts and sugar dissolves. Cook 2 to 3 more minutes; remove from heat. In a separate bowl, mix together flour and one cup milk until smooth. Add egg yolks and salt; mix well and stir in remaining milk. Add flour mixture to brown sugar mixture in saucepan. Cook over medium-low heat until thickened, stirring constantly. Remove from heat; stir in vanilla. Spoon filling into crust; chill thoroughly.
To make caramelized sugar bat pieces, melt 1/3 cup granulated sugar in small saucepan without stirring. Drizzle over a piece of lightly greased aluminum foil. Cool; break into pieces. Top cooled pie with whipped cream and sugar bat pieces.