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 green.
Fortunately bananas are a climacteric fruit, meaning they will ripen after picking, as will peaches, pears, plums, tomatoes, cantaloupe and honeydew. Place green bananas in a paper sack–a plastic bag won’t allow the fruit to breathe–and in two or three days, when the fruit is mottled and aromatic you’re ready to make pudding.