Make banana caramel: In a medium saucepan, bring sugar, corn syrup, and 1/4 cup water to a boil over high heat (do not stir). When sugar starts to darken in 1 spot, carefully swirl pan to caramelize evenly until medium amber in color.
Add bananas and cream (mixture will bubble up furiously); stir to mix. Reduce heat and simmer, stirring occasionally, about 30 minutes. Stir in butter. Let cool, then chill airtight at least 2 hours.
Make pastry cream: In a small pan, heat milk and vanilla bean over high heat until starting to boil. Remove from heat and let sit 15 minutes.
Whisk sugar, flour, and salt together in a small bowl. Whisk in egg yolks, then gradually whisk in warm milk mixture.
Put mixture in pan and cook over medium heat, whisking constantly. When mixture boils, cook 2 more minutes, whisking (it should be very thick and stiff). Remove from heat, stir in butter, and remove vanilla bean. Transfer pastry cream to an 8- or 9-in. baking pan and lay a piece of plastic wrap directly on surface to prevent a skin from forming. Chill at least 1 hour.
Make meringues: Preheat oven to 300°. Place a 9-in. plate or cake pan on a piece of parchment paper (waxed paper won't work) and trace around plate with a pen or pencil. Lay paper on a greased baking sheet, mark side down. Repeat with 2 more pieces of parchment and 2 more baking sheets.
Reserve 1 cup of the nicest-looking pecan halves for garnish. Put remaining 2 cups pecans, 2/3 cup sugar, and the cornstarch in the bowl of a food processor. Pulse until mixture is fine and crumbly, about 30 seconds. Pour into a large bowl.
Put egg whites and salt in the bowl of a stand mixer and whisk on medium speed until white and foamy. Increase speed to high and slowly sprinkle in remaining 2/3 cup sugar. Keep whisking until stiff peaks form. Using a rubber spatula, fold into nut mixture.
Using spatula, dollop meringue into centers of parchment circles, dividing evenly. With an offset metal spatula, spread meringue outward to edge of circles. Bake meringues, in 2 batches if needed, until golden brown and crisp, about 45 minutes. Let cool completely on pans.
Assemble dacquoise: In the bowl of a stand mixer, whisk cream until it just holds a peak (it shouldn't be too stiff). Whisk half the whipped cream into chilled pastry cream.
Peel parchment from meringues. Set 1 meringue in the center of a cake stand and spread with half the pastry cream. Spoon on half the banana caramel. Quarter 1 banana lengthwise and lay on top. Repeat with second meringue, remaining pastry cream and caramel, and another banana.
Set last meringue on top and dollop remaining whipped cream in the center. Quarter last banana lengthwise and lay over cream. Sprinkle with half the reserved pecan halves and put the rest in a small bowl to pass at the table. Serve immediately, using a serrated knife to cut slices.
Make ahead: It's easier to create this dessert if you make all the components ahead and then assemble them shortly before serving, starting with step Chill banana caramel and pastry cream for up to 4 days. Store meringues airtight at room temperature for up to 2 days.
Note: Nutritional analysis is per serving.