Preheat the Oven - Set the oven rack to the middle position and the temperature to 200ºF (93ºC).
Make the Custard - In a large shallow bowl, thoroughly whisk together the milk, eggs, egg yolks, brown sugar, vanilla, cinnamon, nutmeg, and salt.
Dip the Bread - Soak bread slices for 15 to 20 seconds on each side. Use a spatula to transfer to a baking sheet. If desired, sprinkle more cinnamon on top.
Cook the Toast - Heat a 12-inch nonstick pan or cast iron skillet over medium-low heat. Melt ½ tablespoon of butter until it bubbles. Add two pieces of bread at a time. Cook until the first side is golden brown, dry to the touch, and lightly crisp, about 3 to 4 minutes. Flip and cook the other side until golden, about 3 to 4 minutes. Wipe out the pan and add fresh butter. Repeat the process with the remaining dipped bread.
Keep the Toast Warm - Transfer the cooked bread to a wire rack set in the sheet pan. Place inside the oven after frying each batch. Do not leave them in the oven for longer than 1 hour, or it may become too dry.
Prepare the Bananas - Slice the bananas on a bias, into ½-inch thick pieces. This should yield about 2 cups.
Make the Caramel Sauce - In a large skillet, add the sliced butter. Turn the heat to medium, tilting the pan as needed. Once melted, add the brown sugar and cinnamon. Stir and cook for 1 minute.
Add the Banana Liqueur - Slowly add the banana liqueur, stir to combine. Cook until the sugar dissolves, about 30 seconds. The mixture will be bubbly.
Caramelize the Bananas - Add the sliced bananas to the pan, reduce heat to medium-low. Use a spoon to occasionally drizzle some of the sauce on top, cook for 60 seconds. Turn the bananas over, and cook until they soften but do not become mushy, about 30 to 60 seconds.
Add the Rum - Turn off the heat and carefully add the rum to the middle of the pan. Turn the heat to medium and cook the bananas, gently stirring, until most of the alcohol smell is gone, about 15 to 20 seconds. The sauce should glaze the fruit. Turn off the heat. Alternatively, Flambé the Rum - Turn off the heat and carefully add the rum to the middle of the pan. Immediately turn the heat back to medium until the sauce's edges are bubbly, about 3 to 5 seconds. Working quickly, carefully place a long-reach lighter about 1-inch above the sauce on the side of the pan. Move the flame as needed to ignite. Once the flames appear, gently shake the pan until the fire subsides, about 15 to 20 seconds. If desired, sprinkle cinnamon over the flames. It may show some tiny sparks.
To Serve - Remove the French toast from the oven and transfer it to serving plates. Spoon some of the bananas and sauce on top or serve on the side. Sprinkle with chopped nuts.
Serving Size: 1 bread slice and topping
Toast bread if not stale: Place the bread on a wire rack set inside a baking sheet. Toast until dry to the touch but not browned, 5 to 7 minutes per side—alternatively, dehydrate slices in a toaster on the lowest setting.
Omitting Alcohol: After cooking the butter and sugar, turn heat to low and stir in 1/2 cup heavy whipping cream, cook for 15 seconds. Do not skip the cream, it's needed to make the sauce pourable. For flavor, you can add 1 banana extract and 1 teaspoon of rum extract.
For a Creamier Sauce: At the very end of cooking the caramelized bananas, turn off the heat. Stir in 1/2 cup heavy whipping cream.
Storing: French toast can be stored in the refrigerator for up to 3 days and in the freezer for 1 month. The sauce is best enjoyed the same day.
Reheating: Microwave in 15-second intervals until warm. Alternatively, toast until the bread is warm and the surface is crisp.