Prep the dish and oven: Heat oven to 325°F (165°C).
Lightly butter a 2-quart baking dish (about 8x8 inches or similar). Set aside.
Slice the bananas: Peel and slice bananas into 1/4-inch rounds. Arrange evenly in the bottom of the baking dish.
If you like extra texture, reserve a few slices to layer on top later.
Make the custard base: In a medium bowl, whisk eggs until smooth. Add sugar, brown sugar (if using), cornstarch, vanilla, cinnamon, and salt. Whisk until no lumps remain.
Slowly whisk in the milk until fully combined and silky.
Assemble: Pour the custard mixture over the bananas. Tap the dish gently on the counter to release air bubbles. If you reserved banana slices, lay them on top in a simple pattern.
Bake gently: Place the dish on the center rack and bake for 35–45 minutes, until the edges are set and the center still has a slight wobble. Do not overbake—the custard will continue to set as it cools.
Cool and rest: Remove from the oven and let cool on a rack for at least 20 minutes.
Serve warm for a pudding-like texture, or chill for 2–3 hours for a firmer slice.
Finish and serve: Sprinkle with crushed vanilla wafers or a pinch of cinnamon, and add whipped cream if you like. Spoon into bowls or cut into squares once set.