Bring a pot of water to a boil to blanch the basil and mint. Prepare a bowl of ice water next to it. Once boiling, add the basil to the pot and cook for 10 seconds. Remove it and immediately place it in the ice bath. Leave it in there for a few minutes to make sure it is cold, then remove it and squeeze excess liquid from the leaves. Chop the basil and mint into pieces.
Place the basil and mint in a high powered blender or food processor. Add the lime zest, olive oil and salt and puree until the oil is smooth and green. It may be frothy, so let the oil sit for 30 minutes. After 30 minutes, strain it through a fine mesh sieve or cheesecloth to remove the basil bits. Ues a spoon to push any oil through the sieve.