In small mixing bowl, combine eggs, vanilla and milk. Whisk to combine.
Using a non-stick skillet, melt butter over medium to medium low heat.
Dip each slices of bread into egg mixture and then place on non-stick skillet. Cook for two minutes on each side or until golden brown. Continue this until all slices of bread are cooked. Set aside.
Using the same skillet, melt remaining butter with the brown sugar, vanilla, cinnamon and rum. Cook over low heat until smooth. Add banana slices and cook on each side for 2 minutes.
To serve, stack slices of French toast on serving plate. Drizzle with sauce and bananas. Top stack of French toast with a scoop of vanilla bean ice cream and sprinkle with praline pecans.
