Put your asparagus upright in a couple of inches of water. It will stay fresher several days longer than conventional methods.
Source: Williams Sonoma cooking class
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This is a food tip to store asparagus and tomatoes. I find if you keep tomatoes in a dish on your counter, they taste better and ripen thoroughly. If you keep them in the refrigerator, the taste is not as great, and the ripening process changes.
To keep asparagus fresh, I wet a paper towel and wrap it around the bottom of the bunch and secure it with the produce rubber band. I put it back in the produce bag, roll it around to press out the air, fold the top over and put a rubber band around the bunch to keep the plastic tight.
Choose firm straight stalks with firm tips. Avoid stalks that are too thin (1/8 inch) or thick (1/2 in). Wrap the base of stalk with wet paper towels and place into a tight container.
My favorite way to store asparagus is to wrap the root ends of the asparagus with wet paper towels. Do not wet the asparagus, it must be dry. Rubber band or tie the asparagus in a bunch or bunches.
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Select tomatoes that are firm, glossy, and plump. Avoid those that are diseased, soft, bruised, cracked, or otherwise damaged.