The distinction we make between the physical and the mental is problematic on several levels, but I'm going to go ahead and talk as though it's a straightforward matter.
When I'm eating regular, nutritious, satisfying meals made from real food (i.e. when I'm cooking for myself regularly), my desire to binge goes way way down. My cravings for desserts are manageable instead of monstrous.
This won't surprise many people, but it surprises me.
And the only reason it surprises me is that I spent so many years focused on my mental-emotional problems as they pertained to binge eating disorder that I no longer thought of the disorder as having much of a physiological aspect. In a weird way, I acted as though I didn't have a body at all--just a mind that was abnormal. Just emotional problems. Just a problematic psychological history. Just easily triggered because of neural wiring.
While all that stuff plays a big role, I think I'd be better off to conceive of my food/eating problems as half physical, half mental. Of course this is an abstraction, but it's a helpful one! Feeding my body adequate amounts of good food on a regular basis takes care of half of it. Dealing with my brain crazies takes care of the other half of it.
I really disliked Overeaters Anonymous, but I do recall my sponsor telling me on different occasions that I wasn't eating nearly enough for my meals. She was right, and I can see now why she thought it was an important point.