Basil is tough to grow indoors without pretty specific conditions. The thing is, it likes hot temps (more than average room temp); and lots of direct light. I'm sure it can be grown indoors if you pay attention to those, such as if you had a heated greenhouse, but most don't have the needed setup.

It was somewhat slow growing in my basement under the lights, probably due to the temperature (cool down there). That said, it was certainly harvestable and usable. I'm planning on growing it again.

Can you buy a small plant instead? My basil cuttings thrive in a north window in a vase of water. I always tend to cut too much when I make pizzas.

An idea I have read of in an article, by a gardener I rate, but haven't tried myself is to grow basil as sprouts. You sprinkle seed on damp medium and cut it when it is no larger than cress ie 1 - 2 inches. You do this repeatedly through the winter. That way you get the basil flavour but do not have the trouble of keeping larger plants healthy in sub optimal conditions. This is possible on a window sill - no lights needed. It doesn't matter if it is etiolated because you are not trying to grow a mature plant.

I like that idea Flora. It might be worth a try one of these days.

I like Flora's idea and I have plenty of seeds to try it. I put some of the seeds into a pot and brought it in to see what happens. It is only in the 60's at night right now and is expected to get back into the 70's at night by this weekend. I cut the plants that bolted below the seed pods and transplanted all of them into a larger pot. I also pulled quite a few leaves and are drying them now. Thanks everyone for the tips. One way or another I should have fresh or dried basil for the winter.

Basically--you're growing microgreens. And it does work well. I have the best luck using shallow plastic trays with clear lids that takeout foods come in for microgreens (DH is a chef and likes to play with such as that). His other favorite is sunflower mg's. It takes very little soil, as you're only growing them to sprout size. They do grow better if you have a direct light source (as in seed starting) but they're just slower if you don't.