1. Peel 2 bananas and slice into 1/2-inch-thick pieces. Melt 1 tablespoon butter in medium saucepan over medium-high heat. Add sliced bananas and cook until they begin to soften, about 2 minutes. Add half-and-half, bring to boil, and boil for 30 seconds. Remove from heat, cover, and let sit for 40 minutes.
2. Whisk granulated sugar, egg yolks, and salt together in large bowl until smooth. Whisk in cornstarch. Strain cooled half-and-half mixture through fine-mesh strainer into yolk mixture—do not press on bananas—and whisk until incorporated; discard cooked bananas.
3. Transfer mixture to clean medium saucepan. Cook over medium heat, whisking constantly, until thickened to consistency of warm pudding (180 degrees), 4 to 6 minutes. Remove pan from heat; whisk in remaining 3 tablespoons butter and 1 teaspoon vanilla. Transfer pastry cream to bowl, press greased parchment paper directly against surface, and let cool for about 1 hour.
4. Meanwhile, roll pie dough into 12-inch round on lightly floured counter. Transfer to 9-inch pie plate, fold edge of dough under itself so edge of fold is flush with outer rim of plate, and flute edges. Refrigerate for 40 minutes, then freeze for 20 minutes. Adjust oven rack to lower-middle position and heat oven to 375 degrees.
5. Line chilled pie shell with 12-inch square of aluminum foil, folding foil over edges of dough. Fill with pie weights and bake for 20 minutes. Carefully remove foil and weights, rotate plate, and continue baking until crust is golden brown, 7 to 11 minutes. Let cool to room temperature.
6. Peel and slice remaining 3 bananas 1/4 inch thick and toss with orange juice. Whisk pastry cream briefly, then spread half over bottom of pie shell. Arrange sliced bananas on pastry cream. Top with remaining pastry cream.
7. Using stand mixer fitted with whisk, heavy cream, confectioners’ sugar, and remaining 1/2 teaspoon vanilla on medium-low speed until foamy, about 1 minute. Increase speed to high and whip until stiff peaks form, 1 to 3 minutes. Spread whipped cream evenly over top of pie. Refrigerate until set, at least 5 hours and up to 24 hours. Serve.