There doesn't seem to be a trigger for this happening per se, but sometimes part of the cooking interface just… vanishes. On desktop, it's everything in the sidebar except for the NPC, and on mobile it's the pot, current cooking item, and claim box. The most recent time I had this happen, it was when cooking the meat the rabbits drop in Explore, and while I usually put 12 of an item in at a time for a full pot, I don't remember how far along it was when this happened.
Refreshing the page generally gets everything to show up again.
Desktop is Win 10 Firefox, mobile is Android Firefox, and I tend to use my browser pinned to half the screen at 90% zoom (wouldn't be surprised if that's related somehow, though it doesn't have relevance to why mobile might be affected…)
@vihuff, you mentioned this happened to you too, mind adding your setup specs/any details you noticed?