I have tried to dry basil by hanging it on the herb line in the kitchen but the leaves just go black. So I tried chopping them up and freezing them in cubes with water. This worked but could leave some recipes watery if not cooked for longer. One day I chopped up the basil and put it into the ice cube trays and added olive oil. I didn't know if the oil would freeze but it worked. And you have a tablespoon of oil with your herbs to cook with.
Here is how you do it.

1. Take your basil leaves, a few at a time and roll them up.

2. Chop them finely with a sharp knife. Turn 90 degrees and chop the opposite way.

3. Place a teaspoon full of Basil into each section of the ice cube tray.

4. Cover with olive oil.

5. Place in the freezer.

I take mine out of the tray and store in plastic bags in the freezer. I normally use one or 2 cubes depending on what I am cooking.