How I would do it is to go to the heads that are opening and beginning to release seed, cut them with several inches of stem, place them in a clean paper bag, and set it in the shade for several days. I would then tease the seeds out of the heads with a butter knife, proceed to remove the fluff from the seeds, and dry the seeds on a plate in the shade for several days before sealing in a plastic bag for storage.
If I wanted to keep them viable for more than a couple of years I would do a final 3 day drying in a jar with silica desiccant and keep the seeds sealed in a jar in the refrigerator, in the back near the bottom.
The closely related cardoon was found to drop to 50% seed viability after 7 years.