To make the pudding: Preheat oven to 300 degrees F.
Fill ten 6-ounce ramekins with the banana bread cubes, set aside.
In a medium sized saucepan bring the cream to a simmer. Turn off the heat and add the chocolate. Swirl the pot gently so the chocolate is completely covered by the cream, cover the pot and let sit for 3 minutes. Whisk the cream and chocolate together until smooth. Add the half and half, brown sugar, rum and vanilla. In a separate bowl, whisk together the eggs and yolks. Add the eggs to the chocolate mixture and mix until combined.
Place the ramekins on a cookie sheet. Slowly ladle the chocolate mixture over the banana bread.
You will want to gently push the cubes into the chocolate, so that the bread will absorb the chocolate. Fill the ramekins nearly to the top.
Bake for about 45 minutes, or until the chocolate is set firm on the edges, but the center is still a little soft.
Remove from the oven and allow to sit for 15 minutes before serving. They can be served warm, at room temperature or chilled. You can also reheat them for about 30 seconds in the microwave or 10 minutes in a 350 degrees F oven.
Top with unsweetened creme fraiche at brunch or with your favorite ice cream for dessert.