When I think of Chinese cookies, I think first of fortune cookies then I think of Chinese almond cookies. According to the Nibble, I wouldn't actually be thinking of Chinese cookies - I'd be thinking of Chinese American cookies. The Nibble claims that Chinese almond cookies seem to be a derivation of Chinese walnut cookies and that the Chinese almond cookie was created after the first wave of Chinese immigrants to the US. This is possibly true, but one can't be certain. If China didn't grow almonds, I think this origin story would be more likely. Eatocracy points out that these cookies are popular in some parts of China - the same areas where almonds grow. (Granted, China almonds account for only 2% of almonds grown in the world.)
You can buy Chinese almond cookies in just about any Asian bakery. Some grocery stores carry them, too. If you'd like to try making your own, this recipe seems to be very popular - just know that it uses lard. This recipe calls for shortening and butter. Step by step instructions can be found in this video, but if you're looking for vegan option, you'll want to watch this video instead.