Eat away. The basil pictured is an annual and will die one way or another soon. It could just be ready to move along.

FataMorgana

The brown stems are just mature stems. Nothing to worry about, it's normal. As they age, they become quite woody. I find that propagating from those older stems is even better than doing it with the tender tip cuttings.

Thanks!

The stems get "woody" as the plants mature. You can use the stems in a smoker for wonderful favor in grilled chicken or turkey. The smell however might bring the local narcs around...