I looked around a little bit and found a few things. I don’t have personal knowledge about any of them, and I don’t know whether this will help, but here’s what I found.
These first two posts are from the same thread:
viewtopic.php?p=1046757#p1046757
viewtopic.php?p=1063391#p1063391
This third post is from another thread:
Below is the URL for a list of Catholic churches in Taiwan, many of them using the name “mission.” A couple of churches that use that name are listed as being in Taipei. I don’t know which, or even if, any of the missions on the list make and serve meals, but because Catholic missions often provide food where I’m from, I’m guessing that at least some of them do the same thing here. Anyway, here’s the URL:
You might get more detailed knowledge by sending private messages to the posters whose posts are cited above, and they might know of some places other than the ones they mentioned.
Hope this helps.