(Thanks to Israel21c) Normally basil has a short shelf life, and the plant rarely lives longer than a year. However, the Israeli company Hishtil (“seedling” in Hebrew) has grafted two types of basil plants together. One of the company’s first grafted trees is five years old, and still provides fresh Basil.
http://israel21c.org/environment/basil-by-the-tree-ful/