Sorry, the leaves are done for. They can't be salvaged. The plant's stems don't look like they were hit by the frost much, so it wouldn't hurt to pick off the black leaves and bring the plant inside. It might regrow but it probably won't.

Rodney

Technically the leaves are edible. Only got frost bite. This s similar to if you had freezed them(as whole , as paste).
Another option is to dry them.

It's done, any time the leaves turn blackish, it's done. if there were some leaves that are still all green, use them.

I agree that they're probably not harmful if you do eat/use them, but probably not worth it either. Basil does freeze for further use, but it's at much lower temps and in a more controlled manner--yours is just frostbit and will get mushy fast. They won't dry well at this point.

Judging by the size of the stems, your basil is already pretty mature and close to the end of life anyway, so I don't think it's worth it to try and trim and bring inside.

I agree to discard. The point of preservation for me is a superior product to what's available commercially.

There's much better color retention and preservation for frozen basil if leaves are briefly blanched or if it's chopped and frozen in cubes with water.

Carol

Yeah, that seems pretty far gone. If it had a few solid fresh green leaves i would remove the damaged ones and bring it inside in a sunny, full all-day-sun, southern window. I've had basil plants last through the holidays in the NEast. But the flowers need to be pinched during august or the leaves get a bit leathery. I did pot up a big batch of asian variety this year that is doing well indoors. Seems heartier with smaller leaves not as thin as genovese. Just remember next year to bring it in if you have a nice sunny spot for it.

My basil leaves got killed in the frost, but the flavor remains and I picked them and bottled them as they are just like the dry basil you get in the store. They are flavorful as well. It's kind of like freeze dried as the flavors are compressed.