Make the filling: Melt one tablespoon butter in a skillet over medium heat. Stir in brown sugar, ½ teaspoon cinnamon and bananas. Simmer, stirring occasionally, for 5 minutes until bananas are hot and caramelized. Set aside.
Make the French Toast: In a shallow pan (or pie plate), whisk together eggs, milk, ½ tsp cinnamon, vanilla and dash of salt.
Lay out six slices of bread and top each slice with a couple spoonfuls of the banana filling.
Top with the remaining six slices of bread and press down to make sandwiches.
Heat a large griddle over medium heat and melt a small amount of butter on the griddle to coat it.
Place each banana sandwich in the egg mixture and turn to thoroughly coat. Then, place on the griddle. Cook on each side until golden brown.