Step 1: In a small saucepan, whisk together the cold milk and egg yolk until completely blended.
Step 2: Whisk in the cornstarch and blend until well mixed; add in the sugar and mix again.
Step 3: Turn heat on to medium high and cook; whisking constantly, until mixture begins to thicken and boil. (This takes about approximately 5-6 minutes).
Step 4: Remove from heat and stir in the butter and vanilla. Set aside and let filling cool for about 30 minutes.
Step 5: Add the half of sliced banana to the pie shell.
Step 6: Pour the pudding filling on top of the sliced bananas in the pie shell. Cool at room temperature for another 30 minutes.
Step 7: Cover pie with whipped cream, if desired, and then chill pie thoroughly.
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