Yes, it's very easy. Just take cuttings, either tip cuttings or heel cuttings (which I find the best), dip the cut ends in honey, stick them into the dirt, and stand back and watch them grow. Easy as pie.

Some months back we had a terrific storm which tore my favourite basil to pieces, broke off large branches. I just stuck a few of the broken bits in the ground (no trimming, no honey, and some quite large), and now my son has a nice row of basil in his garden!

Thanks! I will try it then. What does the honey do?

Honey is antibacterial, and it acts in the same way as a rooting hormone gel or powder. Protects the cut end of the stem, and encourages root formation. With basil, it isn't really needed, but might hurry things along a bit.

I like the sound of this Greek Columnar Basil, Steve. Do you know if it has another name?

Will root pretty fast in water too, but it should be planted as soon as it has no more than 1.5 inches of root so the roots are not all 'water-roots'.
I've also had great luck taking cuttings and rooting in straight moistened perlite within 7 days. Each cutting had just 1 set of leaves (basically tip cuttings)...in my opinion he smaller the cutting the easier; less evaporation from the leaves while rooting.

Vera

Ahh, I am having horrible success with the basil in tap water technique. It's been about two weeks and so far three cuttings have totally died, and I had to repeatedly snip off the ends of some that were rotting and eventually throw a couple away since they were getting too short. One of them did bust out with loads of roots, but then all of a sudden the root cluster just turned brown and mushy and I had to cut off the end again.

I'm taking two more different approaches now, one cutting with straight perlite, another cutting in the normal water, and another two of those in plastic clear bags. I'm gonna see what happens, but I'm honestly surprised at how difficult this is

Water may have chlorine or too much iron or be very hard with minerals. I have been successful in rooting some basil stems by just planting in muddy soil in a pot. Same with some branches broken off tomato plants. Growing basil from seeds is more reliable.

Oh my god, the bag method worked like a miracle. It's only been two days and it has grown a quarter inch of roots!

Interesting - please describe exactly how you use the "BAG METHOD" as I would love to try it - Thanks!

Well it's pretty much like making a mini green-house. I stick the basil cuttings in water then stick a plastic bag over it and secure it with a rubber band...then leave it in a place with bright indirect light (indirect light is important). Warmth and humidity seem to be the most important in rooting, and I was having a difficult time since I was doing this in early February when the air was still dry