reseeding/perennial herbs for under an deep overhang

I've got a deep overhang on the house so anything against the house needs watering (right near the kitchen). I've got two patches of ground(each 2-3ft wide, 1.5 feet deep) that would be good for perennial/reseeding herbs. Right now I keep sowing different flowers or veggies there.
It is full strong southern sun with stone walls behind them so they get solid heat and never get as much rain as the slate walkway in front of them.
So I'm thinking meditterrean herbs like heat and usually see recommnedation that they prefer to run on the dry side. If they wre perennial/reseeding that would be great. I'm zone 7/6b
The only herbs that have reseeded for me is Dill and hot chili peppers. Drop a few peppers and next year you'll have plants. Chives grow back effortlessly, sage is good for me and it looks like my lavender is going to come back--though not a cooking herb for me. I think rosemary should be perennial here. Is there a thyme that is perennial? Is there a parsley that is perennial? I've got flat leaf out back that I left in the ground. I can't tell if it is coming back or not--too early to tell. I've had a lot of bad luck with basil turning to black and dying. ANd I've never seen it reseed. I won't do oregano--except in pots, too invasive. I grew coriander(Cilantro) last year but I don't know if it will reseed. I only like the seed. Hate the taste of cilantro. I haven't had much luck with cumin yet but love the spice.
DiGiTAL ViNYL (no email) Zone 6b/7, Westchester Co, NY, <1 mile off L.I.Sound 3rd year gardener
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