Banana pudding in the oven

Ingredients:

• 3 cups whole milk
• 1 and 1/4 cups sugar
• 1/4 cup cornstarch
• 4 large eggs, separate the yolks from the whites and beat lightly
• 2 tbsp (30 g) butter
• 1.5 tsp vanilla extract
• 3 ripe medium bananas (about 0.5 kg), thinly sliced ​​(2.5 cups)
• 50 American wafer cookies
• 1/4 tsp cream of tartar

Preparation:

1. In a large saucepan, heat 2 1/2 cups milk over medium heat until steaming.
   
   In a large bowl, whisk together 3/4 cup sugar, cornstarch, and 1/2 teaspoon salt. Then whisk in the egg yolks and the remaining 1/2 cup milk.
   
   Stir half of the hot milk into the egg mixture. Stir until smooth, then gradually pour the egg-milk mixture into the remaining milk in the saucepan. Heat the mixture over medium heat, stirring constantly, until it comes to a boil.
2. Reduce heat and simmer. Stir constantly until the mixture thickens to a pudding-like consistency, 3 to 4 minutes. Remove from heat and whisk in the butter and vanilla.
3. In a 22 cm square pan, place a third of the pudding, half of the prepared bananas and half wafer cookiesTop with half of the remaining pudding, the remaining bananas, and the cookies. Spread the remaining pudding from the pan as the final layer. Cover with plastic wrap, making sure it touches the surface of the pudding, and refrigerate overnight to soften the cookies.
4. Preheat oven to 350°F (175°C), with the oven rack on the top shelf. In the bowl of a stand mixer fitted with a whisk attachment, beat the room-temperature egg whites and cream of tartar on medium speed until foamy.
5. Then increase the mixer speed and add 0.5 cups of sugar, one spoon at a time. Beat for 15 seconds after each spoonful of sugar, then add the next spoonful. Beat until stiff peaks form. Using an offset spatula, coat the pudding completely with the meringue. Bake for 12–15 minutes until golden brown. Serve the pudding warm or chilled.