Preheat oven to 425°F. Line the frozen pie shell with parchment paper, cover fluted edges with tin foil and fill shell with pie weights.
Bake the pie shell at 425°F for 35 minutes; reduce heat to 325°F. Remove the pie weights and parchment paper, leaving the foil around the edges, and continue to bake at 325°F until thoroughly baked and golden-brown, 15 – 20 minutes more.
In a 3 or 4 quart saucepan, heat 1 ½ cups cream and ½ cup of milk over medium heat until steaming. Keep a ladle or deep spoon at the ready. Meanwhile, sift together the sugar, corn starch and salt.
In a medium bowl, whisk together the egg yolks and remaining 1 cup of milk. Add the dry ingredients and mix until thoroughly incorporated. Ladle about ¼ cup of the hot cream into the egg yolk mixture, whisking continuously. Once incorporated, ladle in another ¼ cup of hot cream. Repeat one more time.
While whisking the hot cream over medium heat, slowly stream in the egg yolk mixture. Continue to cook, whisking continuously, until very thick and creamy, about 10 minutes. When large sections of the bottom of the pot are visible while whisking, remove the pot from the heat.
Scrape the hot cream into a clean, cool bowl, passing through a mesh strainer if desired. Add butter and vanilla extract and stir until incorporated. Cover with plastic wrap and let cool 20 minutes.
Fold bananas into cooled cream and immediately pour into baked and cooled pie shell. Cover the top with plastic wrap, making sure it touches the top of the cream, and chill at least 1 hour.
Just before serving, whip remaining 1 cup cream and 2 Tbsp powdered sugar to medium peaks. Remove plastic wrap from pie and top with whipped cream. Garnish with banana chips, if desired.
