I am far from any kind of expert, but that looks like my carrotwood trees, and Im in Zone 9a.

Looks like a Pittosporum something to me. One of the mock orange types?

Even further from being an expert. :)

Thanks. I think Carrotwood leaves have an indented tip. This doesn't. I usually think of Pittosporum as a shrub, but maybe it can turn into a small tree? Also, when I see Pittosporums, the leaves radiate outward in a circle. This doesn't do that. But indeed, Pittosporum is just zone 8, and our freeze was well below that. So that would account for it almost being killed.

I'm sure pittosporum can be any shape you want it to be but yeah--nobody makes those pittos into trees do they?

Do you remember it ever having berries, fruits, cones, flowers, or anything?

The tops of Pittosporum greenery have a "bloom" shape. That's well understood. These don't. But if you can find a picture of Pittosporum that doesn't, I'll be interested to see it.

I thought we ruled that out. :P

If you are familiar with any features of this tree before it froze, like flowers/fruit/etc.,...

Well, all the pictures I can find of Pittosporum tobira have the leaves radiating out from a central stem.

https://www.google.com/search?q=%22Pittosporum+tobira%22+leaves&source=lnms&tbm=isch&sa=X&ved=2ahUKEwim5u72697xAhXKG80KHS2aDN0Q_AUoAXoECAEQAw&biw=1428&bih=909

That's not what my picture above shows. But I went out and looked at the new growth more carefully, and yes, much of the growth is sorta symmetrical around the central stem. So I guess I'll accept that identification. It may be that new growth is not quite as organized.

That all being said, I do have Pittosporums in containers, and all of them show eight leaves radiating outward from the end of each stem. Might be a different variety, though.