Preheat the oven to 300°F (150°C). Arrange the bread slices on a wire rack set inside a rimmed baking sheet. Bake for 16 minutes, turning the slices halfway through, until the bread is nearly dry throughout. Remove from the oven and allow to cool for 5 minutes. Reduce the oven temperature to 200°F (95°C) to keep cooked French toast warm.

In a large bowl, whisk together the eggs, heavy cream, and cinnamon. Transfer the mixture to a 9 × 13-inch baking dish.

Soak each slice of bread in the egg mixture for approximately 20 seconds per side, until saturated but intact. Lift each slice with a slotted spatula, allowing excess custard to drip off, and place on a baking sheet or platter.

Preheat an electric griddle to 350°F (175°C). Lightly grease the surface with nonstick spray or butter. Transfer the soaked bread to the griddle and cook for 3 to 4 minutes per side, or until golden brown. Move the cooked slices to a baking sheet and place in the warmed oven. Repeat with the remaining bread.

In a large skillet set over medium-high heat, combine the corn syrup, brown sugar, maple syrup, and chopped pecans. Bring the mixture to a boil, then reduce the heat and simmer for 2 minutes. Add the bananas and rum extract, gently coating the fruit with the syrup. Simmer for an additional 1 minute.

To serve, spoon the warm banana–pecan syrup over the French toast and serve immediately.