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To prepare the crust: Roll chilled pie dough into a 12" to 13" circle, and settle it into a 9" pie pan that's at least 1 1/2" deep. Crimp the crust, making either a flat edge with the tines of the fork, or a standup rim using your fingers. Refrigerate the crust for 30 minutes, to relax the gluten; this will help prevent if from shrinking as it bakes.
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Preheat the oven to 375°F. Remove the pie from the refrigerator, and prick its bottom surface all over with a fork; this will help keep it flat. Line the crust with a piece of parchment paper (a 9" parchment cake round works well), and fill with dried beans, rice, pie weights, or the oven-safe, food-safe weights of your choice.
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Bake the crust for 20 minutes. Remove it from the oven, remove the weights and paper, and continue to bake for 15 to 20 minutes, until it's golden brown across the bottom. Remove the crust from the oven, and cool it on a rack while you make the filling.
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To make the filling: In a medium-sized heatproof bowl, whisk together the sugar, flour, cornstarch, salt, and eggs, whisking until smooth.
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In a medium-sized saucepan, bring the milk just to a boil.
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Gradually add the hot milk to the egg mixture, stirring all the while.
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Return the egg/milk mixture to the saucepan, and cook over medium heat, stirring constantly, until the mixture thickens and starts to boil; this will happen quite quickly, so don't leave the stove to do other chores.
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Remove the pastry cream from the heat, and stir in the extract(s) and butter.
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Place the sliced bananas in the bottom of the pie crust. Spoon the hot pastry cream over the bananas, smooth the surface, and cover it with plastic wrap — or with the same piece of parchment you used to line the crust while it was baking.
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Refrigerate the pie until it's completely cold. Give it at least 6 hours; overnight is preferable. As the pie chills the filling will thicken and set.
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Serve the pie cold, with whipped cream if desired.
