1. Preheat oven to 375 degrees. In a large saucepan over medium-high heat, combine half-and-half, milk, vanilla bean, and ½ teaspoon vanilla extract. Heat until bubbles start forming around edge of pan, about 4 minutes. Remove pan from heat. Scrape vanilla beans and pulp from pod into milk mixture; discard pod.
2. Carefully separate egg yolks from whites. (When you make the meringue, it will be imperative to have whites with absolutely no yolk at all or the whites won’t whip up properly.) Set whites aside. Add 2 cups sugar to yolks and whisk until thick and light yellow, about 1 minute. Sift flour into yolks, add salt, and whisk together. Slowly whisk ¾ cup of milk mixture into yolk mixture to temper the eggs. Whisk all of the yolk mixture into milk mixture and return pan to medium heat.
3. Cook until mixture thickens, about 8 minutes, stirring nonstop. There will be some lumps, which is fine. Remove pan from heat and whisk in butter, one piece at a time, until incorporated. Blend pudding with an immersion blender for 1 minute. Press the pudding through a fine mesh strainer to remove any remaining lumps.
4. Slice pound cake ¼-inch thick and arrange in a single layer on a baking sheet. Toast in oven until lightly browned, about 6 minutes. Flip slices and toast 4 minutes more. Remove cake from oven and brush both sides with coffee.
5. Spoon about 1½ cups of pudding into the bottom of a deep 2-quart casserole dish. Layer pound cake and bananas on top of pudding and repeat process, ending with a layer of pudding.
6. In a small bowl, whisk remaining ½ cup sugar and cream of tartar to combine. In a stand mixer fitted with whisk attachment, whip egg whites until thick and frothy, about 2 minutes. With mixer running, slowly add sugar mixture to the egg whites. Add remaining 1 teaspoon vanilla extract and beat until the mixture holds soft peaks.
7. Mound meringue on top of pudding and spread to completely cover and seal at the edges. Using the back of a spoon, swirl meringue into peaks. Bake until peaks are browned, about 5 minutes. The top should be brown while the center of the meringue stays soft and creamy. Let cool for 15 minutes. Serve warm.