In a large skillet, melt the butter over medium heat.
Add the bananas, brown sugar, and cinnamon. Stir lightly to combine. Sauté until bananas turn golden brown. Remove to a separate plate.
Wipe the skillet with a damp paper towel and set back on the burner, turning the heat off.
In a large bowl, whisk together the milk, eggs, white sugar, brown sugar, vanilla extract, and cinnamon.
Dunk two croissant slices into egg mixture and press to coat.