How to Make It
Make the pudding: Whisk together cornstarch, salt, and 1½ cups sugar in a large saucepan. Add ¾ cup milk and whisk until combined. Whisk in the remaining milk and yolks.
Cook over medium-low heat, whisking every few minutes until thickened and the mixture coats the back of a spoon, 13 to 15 minutes. Do not allow to boil. Remove from heat and stir in butter and vanilla. Press plastic wrap directly onto the pudding and set aside to cool.
Make the crust: Preheat oven to 350°F. Line a 9 by 13-inch baking dish with two crisscrossed pieces of parchment paper, leaving an overhang on all sides. Lightly coat the parchment with nonstick cooking spray.
Remove 50 Nilla wafers from 1 box (about 3 cups); set aside. Pulse remaining cookies in a food processor until finely ground, about 20 seconds (you should have about 4 cups packed crumbs). Add melted butter and a pinch of salt and pulse until combined, scraping down the sides as necessary. Using your fingertips, firmly press the mixture into the bottom of the prepared pan. Bake until golden, 12 to 13 minutes. Let cool.
Arrange banana slices over cooled crust (they will overlap slightly). Pour half of the pudding mixture (about 3 cups) overtop, then top with reserved Nilla wafers. Spread remaining pudding overtop. Press plastic wrap directly onto the pudding and refrigerate until firm, at least 6 hours or overnight.
Just before serving, make the meringue: Fill a medium saucepan with an inch and a half of water and bring to a simmer. In the bowl of an electric mixer, combine the egg whites, cream of tartar, and 1¼ cups plus 1 tablespoon sugar. Place the mixing bowl over the saucepan, being sure the bottom of the bowl isn’t touching the water. Cook, whisking constantly, until the sugar is dissolved, the mixture feels smooth, and is warm to the touch, about 3 minutes. Transfer bowl to an electric mixer fitted with a whisk attachment and add a pinch of salt. Whisk on low speed until just combined, then whisk on high speed until peaks are stiff and glossy, 5 to 6 minutes.
Preheat the broiler. Remove the pie from the refrigerator and spread the meringue over pudding, being sure to spread all the way to the edges so that no filling is exposed. Broil until the meringue is lightly browned, 2 to 3 minutes. (Alternatively, you can use a kitchen torch to toast the meringue).