There are quite a few mom and pop places that offer hand-made dumplings. Qi Cai - if it's the same as what I am thinking - is a slightly menthol-tasting Chinese green. It's not available fresh here in U.S. but I have seen it in the frozen food sections of Chinese groceries. Gourmet Food in Chinatown offers quite a few selections of handmade dumplings - garlic chive, celery, etc - but I can't recall if qi cai is one of them. Some places offer these frozen to-go. Try these places:
Gourmet Food - 210 W. 23rd Street, Chicago, IL, 60616, 312.842.3366
Dim Sum House - 2610 S. Wentworth, Chicago, IL, 60616, 312.842.5400
Potsticker House - 3139 S. Halsted, Chicago, IL, 60608, 312.326.6898
Katy's Dumpling House - 665 N. Cass, Westmont, IL, 60559, 630.323.9393
I believe that Wei Chuan brand of dumplings also offers a qi cai dumpling. It's machine made but it would be the kind for which you're looking.