This technique can be used for making infused oil whether the ingredient is basil, rosemary, oregano, garlic, chiles, chervil, chives, cilantro, mint, mushrooms or citrus fruit. (Tarragon works best in early spring, otherwise it is quite bitter when infused.)
The ratio of olive oil to flavoring ingredient of your choice is one cup of oil to two cups of tightly packed soft leaved green herb. I rarely make an entire cup of infused oil as it should be used within a week, I usually use 1/2 cup of oil which calls for only one cup of herbs, or other ingredient as listed above.
Fill a large bowl with ice water, set aside.
Bring a large saucepan of water to a boil. Add the herbs, blanch for 5 seconds (make sure the leaves are submerged.) Drain into a strainer and immediately plunge the herbs into the bowl of ice water until cold. Drain the herbs well and squeeze out all liquid.
Puree in a blender with olive oil (blender works better than a food processor here.) Strain puree immediately through a fine-mesh strainer. Strain again through three or four layers of cheesecloth (rinsed in clear water and squeezed dry before straining the herbs.) Put the oil in a sterilized glass bottle, cover tightly and refrigerate. For best flavor, use within one week.
For most purposes I don't mind if the oil is not transparent so I simply drain through two fine metal sieves, one placed inside the other ~ it catches most of the herb sediment.
It is imperative that no fresh herbs (or any other flavoring ingredient you are using) are added back into the oil before bottling because this could introduce the risk of the food borne illness, botulism.
This method is adapted from Michael Chiarello.