Step 1
Combine 2 cups cream, the milk, 1/2 cup sugar, and vanilla bean and seeds in a large heavy-bottomed saucepan over medium heat. Bring to a gentle boil, whisking to dissolve sugar. Remove from heat.
Step 2
Combine egg yolks, eggs, cornstarch, and 1 cup sugar in a medium bowl; whisk until pale yellow in color. Set aside.
Step 3
Whisk 1 cup hot cream mixture into egg yolk mixture. Gradually add egg mixture to hot cream mixture, whisking constantly. Bring to a simmer, stirring constantly with a large wooden spoon to cook out cornstarch and thicken mixture, about 5 minutes. (The mixture may separate slightly; if it does, remove from heat and beat with an electric mixer until thick and smooth.) Strain through a fine-mesh strainer into a clean bowl. Cover with plastic wrap, pressing down against surface to prevent a skin from forming. Chill in refrigerator about 4 hours.
Step 4
To assemble, spread 1/2 cup custard over bottom of prepared crust, smoothing with the back of a large spoon or rubber spatula. Arrange enough banana slices (not quite one-third of them) in a tight, tiled pattern over custard, pressing down with hands to pack them firmly. Repeat to build a second layer, using 3/4 cup custard and enough bananas to cover, smoothing down layer evenly. For third layer, spread 3/4 cup custard over bananas and top with remaining bananas, starting 1 inch from outer edge and working toward center. Spread 1 cup custard evenly over bananas to prevent discoloration. Cover with plastic wrap and chill at least 4 hours or overnight.
Step 5
Whip remaining 2 cups heavy cream in a medium bowl until soft peaks form. Add remaining 2 teaspoons sugar and vanilla extract and continue to whip until stiff peaks form.
Step 6
Remove pie from refrigerator. Fill a pastry bag with whipped cream and pipe onto pie. (Alternately, spread whipped cream evenly over pie.) With a sharp knife dipped in hot water, cut pie into 10 equal slices. Transfer slices to dessert plates. Serve.
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