There are a number of carrot relatives which you can tell by the distinct umbel that forms it's inflorescence. Parsnip seed can be produced in the same manner as carrot seed. Producing your own seed allows you to have fresh seed which is important since parsnip seed tends to decline rapidly in viability. Like carrots, it's a two year process. Parsnips do not cross with carrots; however, nor Queen Anne's Lace so you'll have to worry about isolation for purity only if you are growing more than one variety or if all your neighbors are growing parsnips for seed.
Not likely you say? I decided to look for more than the usual two or three varieties of parsnip available in the U.S. by going to my British sources. To my amazement, parsnips must really be a big deal in England. It was easy to obtain a dozen different varieties from the Exhibition Size to tiny miniature parsnips. Hollow Crown, extended crown, wide or narrow, British growers know their parsnips. I can't understand why they're not more popular in the U.S. Harvested after frost, the roots can be sweet enough to eat them raw or in salads. I really like them oven roasted with potatoes, onions and chunks of winter squash. A great winter time feast.
The yellowish flowers develop earlier than carrots in the second year and the umbel remains flat as the seed ripens instead of curling up. You'll see the ripe seeds out in the open where you can easily remove them for storage.
Seeds that decrease in viability quickly should be carefully stored. In general, when you are storing garden seeds, like Bob Dylan recommends, keep them in a cool, dry place. Cool, like a refrigerator or a cool basement; dry as sealing the perfectly dry seed in a closed jar on a dry day when the humidity is low. Try and maintain a constancy of temperature. By the way, when you are saving your own seed don't seal them for storage until the seed really is dry. Dry enough to shatter, dry enough to break. I will keep seeds that I process drying on screens or in open paper bags for weeks in a dry, controlled environment. During that drying time, day temperatures in the 80's and 90's only help the process, but humidity or moisture can ruin a batch of seed and sealing seed in a container when they have not dried enough can be disastrous for the seed's survival.