Step 1

For the dough, in a large bowl, combine the flour, granulated sugar, and salt. Sprinkle in the butter pieces and cut them into the flour with a pastry cutter (or 2 knives or your fingertips) until the mixture is crumbly and the pieces are the size of small peas. Mix in 5 tablespoons very cold water and toss with a fork until the dough just comes together.

Step 2

Place the dough on the floured counter and knead a few times, just to make a ball. Don't overwork the dough or the crust will be tough! Lightly flour the counter. Flatten the dough into a disk and wrap in plastic. Let it rest in the refrigerator for at least 15 minutes. (If making more than 1 hour ahead, let it rest on the counter for 10 minutes before rolling out.)

Step 3

Roll the dough out on a floured surface into a 12-inch circle. Fit into a 9-inch pie plate and trim to a 1/2-inch overhang all around. Fold the overhanging dough under itself and crimp with a fork or your fingers. Chill the pie shell in the refrigerator for 30 minutes.

Step 4

Preheat the oven to 400 degrees F. Cover the shell with a piece of parchment paper and fill with dried beans or pie weights. Bake on the bottom rack until the crust is set but still blond in color, about 20 minutes. Remove the paper and beans or weights and bake until the crust is golden brown, 10 to 15 minutes more. Let cool completely on a rack.

Step 5

For the custard, in a saucepan, combine the granulated sugar, flour, and salt. Add the milk gradually while stirring. Cook over medium heat, stirring constantly, until it begins to bubble. Cook, stirring, for 3 minutes, or until it forms firm peaks.

Step 6

Stir a small amount of the hot milk mixture into the beaten egg yolks in a small bowl. This will temper the yolks so they don't turn into scrambled eggs. Stir the tempered yolks back into the rest of the custard. Cook for 2 more minutes, stirring constantly. Remove from the heat and stir in the butter and vanilla. Slice 2 bananas into the cooled pastry crust. Top with half of the custard and slice the remaining bananas on top. Top with the rest of the custard. Chill for at least 1 hour.

Step 7

For the whipped cream, in a cold bowl with an electric mixer, beat the cream, confectioners' sugar, and vanilla until firm peaks form. Be careful not to overbeat or your cream will turn to butter. Watch as you beat and stop when it gets thick and stays on the beaters when you remove them from the bowl.

Step 8

Top the pie with the whipped cream and serve.