Listen to your Brother Jesse.
Do not make banana pudding with green bananas. Even if the fruit has a tinge of green on the ribs, the banana will be hard and bitter. You must use bananas that are ripe.
Now, you’re not going to find ripe bananas in the grocery store–sometimes I think the public has been conditioned by years of buying green bananas that any banana with a dark spot is spurned–so you’re going to have to buy them a bit green. Fortunately bananas are a climacteric; they ripen for a while after picking. Daddy, who was stationed in the Pacific during WWII, and knew quite well how a ripe banana tasted– put bunches on top of the refrigerator–where we couldn’t reach them–to ripen.
Place grocery bananas in a paper sack–plastic doesn’t let the fruit breathe–and in two or three days, when the fruit is soft and aromatic you’re ready to make banana pudding. Or banana pound cake.
Hell, just to even eat, for that matter.