Combine corn starch, sugar and salt in a 2-quart saucepan. Gradually stir in milk until smooth. Stir in egg yolks.
Bring to a boil over medium heat, stirring constantly, and boil 1 minute. Remove from heat; stir in vanilla.
Spoon small amount of hot filling into pie crust. Top with bananas and remaining filling. Cover surface with plastic wrap. Cool completely on wire rack.
Spread whipped cream over filling. Refrigerate for 1 to 2 hours before serving.