Beat the eggs, milk, sugar, vanilla, and cinnamon together in a mixing bowl until well blended. Pour the egg mixture into a baking pan large enough to give you room to turn and soak the bread. (A 13 by 9-inch pan works well.)
Lay the bread slices in the egg mixture and let them soak, turning them several times, until the bread has soaked up all the egg. Turn them gently so they don't break apart on you.
Heat the butter in a large nonstick skillet over medium-low heat. When it starts to bubble, lay the soaked bread in the pan. Cook, turning once, until the bread is nicely browned and the egg in the center of each slice is cooked through, about 12 minutes. Serve warm with the Orange-Rum Bananas.
Heat rum, sugar, butter and orange juice in a large skillet until the butter is melted. Add the bananas. Bring to a boil over medium heat, then lower the heat so the sauce is bubbling gently. Cook until the bananas are softened, about 4 minutes.
If your skillet isn't large enough to hold all the bread slices at once, cook them in batches. Before you start your first batch, preheat your oven to 200 degrees F (or "Warm"). Keep the cooked slices warm on a baking sheet in the oven while you cook the rest.