I planted some basil last year called globe basil.I do the same thing. I love the way it smells. I could grow herbs just for the aroma therapy. I love the smell of fresh basil too. I'm looking for a climbing plant that looks good over winter too. I plan on putting up some fence but thought to make it more private I'd plant something on it. I absolutely hate morning glory! That stuff is so invasive. I thought about honey suckle.... maybe even some grapes, but I'm worried they would get to heavy.
It grows in a ball shape, has a Lemonish background flavor and teeny tiny leaves.
What about jasmine? I don’t know if it grows where you are though?