Answer: Let the plants finish blooming and setting seed. Unless it is from a hybrid variety, it should come fairly true to seed. While they are blooming, the beneficial insects in your garden including hover flies and some non-stinging wasps will thrive on them. Once seed heads begin to brown, cut them and place in an open paper bag in a dry location to fully dry. Later shake heads, collect seeds and store in an airtight container in the refrigerator.
Your old plants may be transplantable, but since parsley is a biennial (it dies after setting seed in its second season), you may just want to start with vigorous young plants. I have successfully transplanted Chinese parsley in Texas, but haven't tried it with Italian parsley. If you have the space, it's worth a try. Try to get a large undisturbed rootball when you dig plants and water it in well in its new location.
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