Basil is an annual which means it grows for one growing season. If it is already in a container, you can bring it in to extend your season some but do that before it gets to chilly outdoors. It will probably not last through the winter indoors. If it does, it will be a rather sad and not very robust plant. Some like to take cuttings and root new plants - always worth a try. You can try to save seed from the seed heads if you planted an open-pollinated variety like "Siam Queen." Thai basil is wonderful and is in my gardens each year! FataMorgana

Socks, I do as you said, let the seed pods develop and self-sow, but I also harvest some of the seeds, make sure they are completely dry (not all that easy in our humidity!) and store them in a sealed plastic bag in the refrigerator and plant when the soil is warm--May here in 8b Texas but probably earlier in your zone 9. About every three or four years I buy seed and plant it. Genetic diversity, my silly idea, who knows? Anyway, I like to get a fresh start every few years.

You've already potted it up so enjoy it as long you can. Maybe you can even take cuttings from it. But the plant will eventually become not very productive and not worth the effort. Plant the new starts or seeds come spring for best results. FataMorgana

I've never been able to over-winter herbs in my house. (I'm in Long Island, part of the cold NorthEast). It just gets too dry in winter, I tend to keep the heat up in my home. My daughter and I also seem to get sinus problems and nosebleeds in winter from the dry air. So I treat basil as an annual, buy new plants every spring. I grow basil in a container on my patio. I do enjoy being able to walk outdoors with a scissors and snip fresh basil leaves for salads and sauce. One of my favorites is Marinara spaghetti sauce (any canned/jarred brand will do) with torn basil leaves added about five minutes before serving.