George Carlin covered this back in the 70's. You can make fun of your own ethnic group, but you shouldn't cross over to other groups. As a writer and former stand up comic, I've always had to step back and weigh the joke. A lot of my Irish, German, and Scottish jokes could be considered racist were it not a part of my heritage. I can even slip in English, Dutch, Welsh and Viking jokes. Any other ethnicity, though, I have to think very hard about because I'm not representative of those groups. My grandsons, though, can not only hit on the groups I mentioned, but add French and African to their repertoire. Funny, as one of them is blond haired and blue eyed. One grandson and three grand daughters can also add in Native American. A niece and nephew technically could tell Asian jokes as they were born on base in Okinawa, but I've not heard them do that.
The key to poke fun at your own heritage, though, is to make sure the reader understands upfront that you're ribbing your own people. This joke, for example, I'd rate on a scale of 1 - 10 a 6. It comes across as anti-Asian. Not knowing your Asian heritage, it would be interpreted here as being a form of racist hate joke. I paid the upvote tax to comment, and then, only after going through your profile and discovering you're playing with your own heritage. So why did I revert to using a stereo type Asian in my comment? I'm not Asian. Remember, I said I have to weigh any ethnic joke outside of my group. I felt it was a better response to show a brown, fat Asian kid to represent that stereo types often aren't as they are presented. So why the pigeon Engrish? More to emphasize the point of stereo typing.
Oh, one other group I've found that I can rag on: Rednecks. Come from a long line of those, as do many of my friends. Not only that, but I've discovered that I can do redneck humor about any other culture to show that it's universal. Here's a link to a video I did a few years back about Rednecks around the world. You'll see Rednecks from America, Europe, and Asia represented here: https://youtu.be/p9W--_RSces
