What is certain is that they are not a Japanese invention. The dish they call menchi katsu belongs to meals known as "yōshoku", which are adaptations from Western culture. In Japan, they are ...
From Marc, Salmon Menchi-katsu: deep-fried breaded salmon cakes! Maki cooks up a delicious Chicken-nasu bento with her 3S sauce plus one. Also, a look at Taiwan's "san-bei" or "three-cup" cuisine.