Preheat oven to 375 degrees. Place the milk, half and half, and vanilla bean pod in a large saucepan. Place over medium-high heat to scald it. It will be ready once bubbles begin to form around the edges of the mixture, about 4 minutes. Remove from heat. Scoop out vanilla bean pod and remove contents by slicing down the middle and, with a paring knife, scrape out the seeds. Add seeds to the milk mixture. Discard pod. Add 1/2 teaspoon of vanilla extract to milk mixture and whisk together. Set aside.
Separate eggs and place eggs whites in a bowl and set aside. Place egg yolks in a large bowl with 2 cups of sugar. Whisk together quickly until the mixture turns a light yellow, about 1 minute. Sift flour and salt over the egg yolk mixture. Whisk to combine. It will take some muscle to mix this together since it's so dense. But don't give up! It will come together.
Slowly whisk in 3/4 cup of the milk mixture to the egg yolk mixture to bring the eggs to temperature without scrambling them. This is called tempering. Add the egg mixture to the rest of the milk mixture in the saucepan. Place back on stove at medium heat. Constantly whisk the mixture as it begins to thicken to prevent lumps. It will take 8-10 minutes for the mixture to thicken into a pudding.
Once the mixture has thickened, turn of heat. Place an immersion blender into the pudding and blend for 1 minute. Then, push pudding through fine mesh sieve to remove any remaining lumps. *Note: if you don't have an immersion blender, I recommend pushing through the sieve twice.
Slice pound cake into thin slices, about 1/4 inch. You should get 16 slices. Place them in one even layer on a baking sheet. Toast in preheated oven for about 6 minutes. Remove from oven and flip over to toast on the other side for another 4 minutes.
Begin layering the pudding by placing 1 1/2 cups of pudding on the bottom of a deep 2 to 3 quart baking dish. Place half of the loaf slices on top of pudding, followed by half of the banana slices. Repeat with a second layer and finish with a layer of pudding on the top. You should have three layers of pudding and two layers each of the bananas and pound cake.
Place the leftover egg whites in the bowl of a stand mixer fitted with a whisk attachment. Begin whisking on medium high until frothy, about 2 minutes. Reduce speed to low and slowly add in remaining 1/2 cup of sugar and 1/2 teaspoon of cream of tartar. Bring speed back up to medium high and continue whisking until soft peaks form. Place all of meringue on top of pudding and begin spreading into an even layer and sealing the edges. Meringue shrinks when it heats so if you don't seal the edges, pudding will be exposed. Using the back of a spoon or spatula, quickly press down on the meringue to create peaks. Bake in the oven to brown the meringue, about 10 minutes. If you don't like yours so brown, bake for 5-7 minutes.
Remove from oven and serve immediately.