I root basil when I start up my hydrponics system for the fall/winter, and again for putting them outside, in the spring. I root them in a cloner, so they are water rootings, and I have never had a problem putting them into soil in the spring. And it cuts easily a month off of the time when started from seeds.
I would cut a half inch or so off the end of the stems, since they aren't new. Then, with a very sharp knife, score the stems horizontally about 1/8" apart - I do this on opposite sides, on about an inch of the stem, and these score lines are where the roots show up! I dip them in a cloning gel, and In the cloner I start seeing them in a couple days, and many are ready to transplant in less than a week.