Don't worry. I had the same problem. I think pests eat the basil making them brown and have holes.. What solved my problem was spraying them with murphys soap spray. Just soak your basil in water before using it, you may have to do that a couple of times and the basil will be as delicious as always. I still use those basil leaves, just rip or cut off the brown part and wash real well to make sure don't have bugs. Also, sometimes I notice after it rains the basil gets like that, I guess somehow the soap comes off from the water or for some reason rain attracts certain pests, so add more after a rain storm. And don't worry, just pick the bad leaves and more will grow. As I said, I use them just take off the bad part.