I agree with immediate consequences, but you said in the title that your charge "started punching" you... but then you said in the actual post it's only happened twice in the past 6 months?
To me, that doesn't scream pattern. It seems like she just used bad judgment twice over a long stretch of time....
That doesn't make an excuse, of course you should punish her each and every time and discuss what happened, but still..

Instill immediate consequences, but talk to her before you do. She's old enough that it sounds like you're trying to be more friendly than authoritative with her (with limited success by your description) so tell her that you know she doesn't mean to hurt anyone when she punches them but the fact is it is painful and inappropriate. Tell her adults don't hit each other and neither to children, so she can't either. Tell her from now on, if she does, she'll be receiving XYZ as a consequence. Then follow through. I bet she'll punch you once, maybe twice to see what's up, and then it won't happen anymore. If it does, she has a bigger anger problem that needs to be addressed.

Absolutely instill immediate consequences. Stern words aren't consequences. Talk to the parents too and see if this is an issue with them as well.

As the above poster said. Why aren't you punishing her for this? "Go to your room and don't come out until you're capable of being around people without punching them, and ready to apologize for the hurt you've already caused just now."

Uhhh consequences??

Hit her back! Unfortunately, you can't but talk to parents and see if she does it to them or her little sister.

I nanny two girls, 7 and 10 years old. Lately the 10 year old has been punching me in the arm kind of hard. She never does it as a result of anger or frustration or anything, she's always just trying to play or joke around. But it's way too hard and it hurts, and what's more troubling is that she doesn't seem to care when I tell her that it hurts.

Any time she's ever hurt me on accident and I say it hurts, she's super quick to apologize and is very sympathetic (she's never hurt me very badly on accident. It's always just stuff like she accidentally stepped on my toe or something.) But when she "playfully" punches me and I sternly tell her to knock it off because it actually hurts and that's not funny, she doesn't say sorry, she usually keeps smiling/laughing and goes back to doing her homework or whatever she was doing.

I have tried dragging it out when she doesn't apologize, saying things like, "I'm serious, that actually hurt my arm really badly and you need to knock it off." She doesn't seem to care.

She doesn't do it often, she has only done it a couple of times in the last ~6 months, but still, that's enough to irritate me and also worry about why she feels the need to intentionally hurt me. I'm a great nanny and the kids totally love me. They're always happy to be around me and so I don't think it's some kind of latent hatred or anything like that.

Any tips?