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You don't really "cook" pomegranates. But you can cook with them. I like to get the arils out by submerging the halved pomegranate in a large bowl of cold water, and breaking it apart. The white bits float and the arils sink to the bottom. When sufficiently broken apart, skim off the white bits, and drain off the water until you can easily grab the arils. Dry them on a paper towel for use. Unfortunately, there is not a pretty way of getting at those sweet morsels called arils.
I agree with the other cook on how to peel using water. Pomegranate arils are a great addition to many cold dishes such as salad. It would probably be a great addition to a Tuscan kale salad. You can even find pomegranate vinegar to make a great dressing. I love to add it to my cereal in the morning. By the way, pomegranates store whole for more than a month. After removing the arils, they maybe dried with a paper towel and stored in a paper towel lined bowl covered with plastic wrap for several days.
I cut the pomegranate crosswise and beat the skin side with the back of a spoon and they fall right out. You have to separate the white part from the anrils I also use pomegranate molasses It is Turkish. Has a nice tart flavor.
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