1. Make the crust: In a food processor, pulse the flour and salt together. Add the chilled butter and pulse until mixture resembles coarse meal. Add ice water 1 tablespoon at a time, pulsing until dough just begins to hold together. Shape dough into a disc, wrap in plastic, and refrigerate for at least 1 hour.

2. Roll out the dough on a lightly floured surface and fit it into a 9-inch pie plate. Crimp the edges decoratively. Refrigerate for 30 minutes.

3. Preheat oven to 400°F. Line the chilled pie crust with parchment paper and fill with pie weights or dried beans. Bake for 20 minutes. Remove the parchment and weights and bake for 10-15 minutes more, until the crust is golden brown. Allow to cool completely on a wire rack.

4. Make the filling: In a medium saucepan, whisk together the milk, sugar, and cornstarch. Cook over medium heat, stirring constantly, until the mixture thickens and bubbles, about 5-7 minutes.

5. In a medium bowl, whisk the egg yolks. Slowly whisk in about 1/2 cup of the hot milk mixture to temper the yolks. Then slowly whisk the tempered yolks back into the saucepan with the remaining milk mixture.

6. Cook, stirring constantly, until the mixture thickens enough to coat the back of a spoon, about 2-3 minutes. Remove from heat and stir in the 2 tablespoons of butter and the vanilla extract.

7. Spread the banana slices in an even layer in the cooled pie crust. Pour the hot custard over the bananas, smoothing the top. Refrigerate for at least 4 hours or overnight.

8. When ready to serve, top the pie with the whipped cream. Serve chilled.