Start the caramel sauce first by combining all of the sauce ingredients in a small saucepan over medium heat. Gently whisk as ingredients begin to melt. The sauce will begin to thicken as it slowly bubbles and boils. The longer you cook it, the thicker it will become. I suggest cooking it to just a little bit thicker than maple syrup. Remove from heat and set aside.
In a medium shallow bowl, whisk together milk, eggs, sugar, vanilla, and salt.
Melt 2 tbs unsalted butter in a fry pan or skillet over medium heat.
One at a time, dredge slices of banana bread in egg mixture. Allow some of the mixture to soak into bread. Place banana bread slice in pan. Repeat with another piece or two. Do not crowd the pan. Cook each side until it starts to darken in color or feel toasty. Add more butter to pan if necessary. Repeat until you’ve made enough.
Serve with sliced bananas topped with caramel sauce.