Thank you for your patience in receiving a response to your question about your basil. Basil leaves can brown for reasons such as; under or overwatering, extreme heat/sun, insects or disease. From the photos it appears as though the only browning is on the top leaves which leads me to think it is from the heat we have been experiencing. I would suggest removing the top leaves that are discolored and see what the new growth is like. Make sure your watering is consistent, but not too much. Test soil by putting your finger down a few inches to see if it is dry. If it is dry water at the base, preferable early AM. This keeps the leaves dry and gives time for it to dry out at the base.