I’m like a magpie when it comes to previously-unknown-to me herbs and spices, so I have a lot of 'em, and I’m not sure what makes one more “unusual” than another, except maybe for their rarity in my native US/Western cuisines, or in the US marketplace?
In that vein, I guess I’d have to go with blue fenugreek (a Georgian spice, as far as I’ve seen, not grown or used elsewhere), and maybe edible camphor? I’ve used the former, which is very similar to regular fenugreek, but has a slightly different fragrance, a little more floral maybe? (But I’m not at all sure I could tell the difference in a dish, even side-by-side). I have not (yet) used the latter, which afaik is only rarely used even in Indian cookery (only in a few sweets/desserts), but it’s not at all easy to find (here), so I grabbed some when I did come across it locally.
Maybe Tajik cumin counts too. I’d never heard of it before I saw it at a local Uzbek grocery store, but according to the Interwebz Tajikistan is famous for it in some circles. I’m pretty sure it’s the same species as regular cumin, just a localized strain (and maybe terroir-specific), and it’s used like/where regular cumin might otherwise be used, but I’d describe it almost as a cross between regular cumin and black cumin. Has a definite earthier edge to it like black cumin has, but not as overwhelming as black cumin. (I don’t know if anyone in South Asia ever uses black cumin in place of the regular kind - the recipes I’ve seen treat them as different flavors - but I myself would not like as a one-to-one replacement for regular cumin.)