If you’re pretty sure you could never have enough basil plants, here’s a way to get some more with every harvest: use a little bit of each stem as a cutting.
Harvest a little more than you need for your cooking. When you pluck leaves from your newly cut stems, be sure to leave the second set from the bottom on. Cut the stem off just above those leaves, and pluck off the bottom set of leaves too.
Immediately place the shortened stems in water. The rest is for cooking.
Find a place with no direct sunlight to set your container full of stems for a week or two. It seems to help if the container is opaque, so wrap it with foil if you need to.
When the stems have roots around an inch long, you can plant them in soil. If you're planting in the ground, you may want to pot them up in small containers for a few weeks first. Be sure to keep the soil extra moist and the young plants out of direct sunlight for a few days until they get used to their new life as independent plants.