This likely refers to “cocotte” [0], the French term for a kind of casserole that might be used for dishes for which that vegetable cut shape is typical — or maybe the shape of the cut is reminiscent of the shape of a cocotte.
English Wikipedia cocotte disambiguation suggests French oven, which redirects to Dutch oven, which is just what Americans call a casserole.
Is it the enamelling, which Wikipedia suggests is sometimes used as a distinguishing feature between 'Dutch' and 'French' ovens? (I've (British) never heard of the latter before.)
Apparently a cocotte is also an 'elegant prostitute'/courtesan, meaning 'small child' before that. So is a cocotte a small casserole, peut être?
It seems cocotte = English 'casserole'; casserole = saucepan.
The enamel vs. cast iron interior of a cocotte IME in the UK is not significant, but in the US going by Wikipedia anyway enamel = French oven; pas d'enamel = Dutch oven.
...I suppose we've no hope of agreeing on all this if we can't even have a 'cup' be the same size! (Or convince Americans that they shouldn't be (and in many cases would find it easier if they weren't) using volumetric measures for everything anyway, for that matter.)
The French Wikipedia article is clearer than the English one : https://fr.m.wikipedia.org/wiki/Cocotte_(cuisine)
Note that a pressure cooker is called a Cocotte minute. Because it cooks quickly.
Cocotte is also a term that can be used for chickens or chicks, but that has nothing to do with cooking utensils.
I'm afraid my French isn't up to reading a Wikipedia entry, which is why I asked (GGP linked the same article).
It's rather that they are false-friends: a french « casserole » is an english ‶sauce pan″ (the most vanilla cookware, a metal pot with a handle).
A cocote has typically more heat inertia (made of thick casted iron), is larger (so you can cook large pieces of meat in it) and thus far less handy.
Par exemple: http://chut-je-cuisine.com/pommes-de-terre-tournees/
As for the cut, I'd hardly call it a Japanese cutting technique.