Prepare the custard base: In a medium saucepan over medium heat, whisk together ¾ cup sugar, flour, and salt. Gradually add milk, whisking constantly to prevent lumps. Cook for 8-10 minutes, stirring often, until the mixture thickens and bubbles gently.
Temper the eggs: In a small bowl, beat the egg yolks. Slowly whisk in about ½ cup of the hot milk mixture to temper the yolks (this prevents scrambling). Pour the yolk mixture back into the saucepan.
Cook the custard: Continue cooking over medium heat for 2-3 minutes, stirring vigorously, until thick like pudding. Remove from heat and stir in vanilla extract. Set aside to cool slightly.
Assemble the layers: In a 9x13-inch baking dish or trifle bowl, layer vanilla wafers on the bottom. Top with a layer of banana slices. Pour half the warm custard over the bananas, spreading evenly. Repeat with another layer of wafers, bananas, and remaining custard.
Make the meringue: In a clean bowl, beat egg whites and cream of tartar with an electric mixer on medium speed until foamy. Gradually add the remaining ¼ cup sugar, beating on high until stiff, glossy peaks form (about 3-4 minutes).
Top and bake: Spread the meringue over the custard, sealing to the edges of the dish. Bake at 350°F (175°C) for 10-12 minutes until the meringue is golden brown.
Chill and serve: Let cool to room temperature, then refrigerate for at least 4 hours (or overnight) for the flavors to meld. Slice and enjoy!