Yes, the Chinese restaurants in the West have this habit of having a Chinese menu, with more authentic dishes which are not available in the menu given to Western/non-Chinese diners. I remembered a time I was in Cologne where, after 2 weeks of Teutonic fare, 3 Singaporean colleagues and I walked into Tchang, Cologne’s oldest Chinese restaurant for lunch. We wanted something Oriental for a change.
The restaurant was packed. The proprietress, who’s Taiwanese, came over and chatted with us in Mandarin, and offered to cook for us dishes “off the menu”, as she said “we won’t eat the things from the usual menu, which are really meant for locals”.
I remembered we waited & waited for our food to come, whilst other tables had their food served pretty promptly - obviously, the chef had to cook dishes which are out of his usual repertoire for our order.
The funny thing that will always stick in my mind was - the moment our orders came (after about 45 minutes’ wait) to our table - a hush fell over the restaurant and we could distinctively “feel” 60 pairs of eyes from the other tables looking at our food. Methinks the Germans were curious as to what we ordered. 
