For filling: In a medium saucepan, combine 1/2 cup of the brown sugar and the 1/4 cup butter. Cook and stir over low heat until butter melts and mixture is smooth. Remove from heat.
In a small bowl, combine the remaining 3/4 cup brown sugar, the flour and cornstarch.
Add flour mixture to butter mixture; stir until combined. Gradually stir in whipping cream. Return saucepan to heat.
Cook and stir over medium heat until thickened and bubbly; reduce heat.
Cook and stir for 2 minutes more. Remove from heat.
In a small bowl, lightly beat egg yolks with a fork. Gradually stir about 1 cup of the hot filling into yolks.
Add yolk mixture to saucepan. Bring to a gentle boil over medium heat, stirring constantly; reduce heat.
Cook and stir for 2 minutes more. Remove from heat. Stir in the 3 tablespoons butter and vanilla.
Pour filling into the Baked Pastry Shell.
Cover surface of filling with plastic wrap. Chill in the refrigerator for at least 2 hours before serving.