This is a simmered dish with the rich flavour of satsuma-age (deep fried fish cakes). Aside from komatsuna, it's also delicious with mizuna leaves or bok choy.
My mother often made this dish. It might be a country-style way of using satsuma-age?
Instead of satsuma-age, you can use abura-age (thin fried tofu), with the oil removed, or atsu-age (thick fried tofu).
Enjoy Japanese food around the world.