It would be easier with the branch in my hands (as you have it), but even from the pictures, it took me about 15 minutes online to google the search terms you were *handed* about this plant, and narrow it down to a few possibles. It took another 10 to go through pictures for the possibles, and get it to one.

(((Are weeping cherry or black tupelo (of all things...) used in South Asian cooking???)))

Now, do your own homework!! Follow the trail of breadcrumbs you were given! Use your brain, and track it down.

Then, if you need to be sure, use your nose. Crush a leaf and smell it. And talk to someone who cooks.

Again..... Do your own homework!

Curry leaves.