I bought organic bananas that were green two weeks ago (really), went on vacation, and they are still green. Please explain!
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Supermarkets use banana gas to ripen the bananas, perhaps the organic store didn't. They won't ripen if there isn't enough ethylene in the atmosphere. You can gas your own bananas by placing in a plastic bag with several apples till they begin to ripen. Is your house cold? cold will inhibit ripening. They may have been cut too green as well.
Put the bananas in a paper bag with an apple. Check every day until they get to your prefered level of ripeness. The apple will give off sufficient ethylene gas to ripen the bananas. Works for avocados too.
I've had success ripening bananas in a paper bag without an apple. So, if you don't have any apples in the house, still give the paper bag a try.
Do you know that bananas, which have no season, are the most-purchased item in the produce department? Do you also know that green bananas can be a good thing?
On the home front, if you want ripening, place the bananas in a bag, preferably paper, or a plastic bowl with its lid resting loosely on top. It's the concentration of ethylene gas that is important, so if you want ethylene quicker, add an apple or two or three; bananas give off ethylene naturally as they ripen, and without an apple in the bag, it will take a little longer for the ethylene to become concentrated. Ethylene is a naturally occurring by-product of ripening and is considered to be organic.
Ripening rooms, in which ethylene or CO2 is pumped in to control the ripening (or not) process of bananas, avocados, etc., are not installed on the supermarket level. They're usually installed in the warehouses of grower co-ops or distributors. While ethylene is a ripening gas, it can also lead to rapid decomposition, which is one reason tomatoes aren't put in the bag instead of apples--apples can survive the higher concentration of ethylene quite well, but tomatoes turn to mush.
Bananas, organic or not, are hacked into saleable-size bunches while they're solidly green and less prone to bruising. They're packed into sturdy but hole-y cardboard boxes lined with heavy paper and "breathable" plastic bags. Sometimes, but rarely, this packing blocks ethylene from reaching every single banana.
As much as the grower tries (it is in his best interest to sell "good" bananas, after all), a bunch that was picked much too early to ripen well will get through his hands. Some fruits and vegetables, when picked too early, go straight from immature to rotten, bypassing the ripening stage completely.
And as much as the grower/distributor/transporter/supermarket/consumer tries, it's not always possible to keep bananas at 57 degrees, their optimum storage temperature. It could be that the bananas were transported in a truck with faulty refrigeration, that they sat on a pallet on a loading dock for 10 minutes in freezing weather, or that they were chilled in the trunk of your car for the half-hour ride home from the grocery store.
No matter who or what disrupted the ripening process, most grocers will give you a full refund or exchange. Or, you can treat them as plantains:
http://www.thecookingadventuresofchefpaz.com/2010/03/31/chifles-fried-green-banana-chips/ (How could you not love a blog with the subtitle "Look Mom, I'm Boiling Water!")
I cut them in half lengthwise, saute them in a bit of butter, sprinkle them with brown sugar, wrap each half in a spring roll (rice paper) wrapper, then deep fry for a Filipino treat.