I grew basil in 2 different containers. I had a huge spider mite problem after I purched Miracle Gro soil in one container. Earlier this year, I harvested all the leaves off completely and leaves grew back. The spider mite problem somehow transferred to the other pot and I did the same, harvested all the leaves and that worked fine but it's been really cold lately in TX, I am not sure if it is bc the basil has flowered before but it's turned woody, completely, as stated in the title. I'm not sure if it's diseased and if I should get start a new batch of seeds now or if there's an oz of home for these growing twigs? It sucks because it was my favorite container of basil too. They were extremely bushy.
On the assumption you were growing outdoors, Basil (Ocimum basilicum) is only perennial in very warm regions; it's a tender annual plant in colder areas. Now that it's cold, it's unlikely to grow again. You've not said precisely which USDA zone you're in, but if you expect even colder weather during winter, then its definitely not going to grow again, so you might as well dispose of the woody brown one. You've not said what condition the other basil plant is in, in the other container, but if your temperatures are either 60 deg F or likely to get lower, then you will lose that one as well.
You can grow it from seed indoors, but as it grows, it will require as much sun as you can give it, see here for more information on Basil growing generally https://www.thespruce.com/how-to-grow-basil-plants-1402624