You hear all the time that eating mindfully helps you eat less. It's true. If you attend to the experience of your food and your eating process as fully as possible, you can be satisfied with less. Start doing it and you'll see the contrast from all those times you wolfed something down while multitasking or otherwise distracted and then thought "That was it? That wasn't enough." And then reached for more food then and there, or perhaps an hour later.
If you want to eat less, pay more attention. If you want to eat more, pay less attention. In my experience (and I'd be interested to hear other views on this), I don't think one can binge mindfully. A binge indicates an unusually large amount of food eaten in an unusually brief period of time, and there's an mental state involved that isn't calm or focused. If your mind is calm and you are eating slowly and attentively, I doubt you are binge eating. It's possible you are still overeating, but I think binging is unlikely.
Ice cream was a classic binge staple for me; I'm still prone to overeating it. Can you believe that it wasn't until I slowed down and tried to eat ice cream mindfully that I realized my mouth became numb after a scoop or two and that I couldn't really taste the ice cream after that point? And that it's not pleasurable to eat ice cream you can't taste? All those years of binging on ice cream a few times a week depended on my inattentiveness; it's how way I was able to remain convinced that I "loved" eating two pints of ice cream in 20-30 minutes.
If you tend to binge while watching TV or movies, browsing, fiddling with the radio in your car, playing games on your phone, letting your mind wander far and wide, whatever...try doing it without your favorite distraction added. You might find that the act of eating itself becomes boring pretty quickly, and that the food doesn't taste as great as you remembered.
I'm convinced that junk food manufacturers depend on people not paying much attention to what they are eating. Eating m&ms in the movie theater is fun. Sitting down at a table and eating one m&m at a time, attentively, is freaking dull. I think fast food tastes good, but it loses much of its magic when you pay close attention to it--say, if you sit down and eat it quietly instead of while driving or talking with another person. And there are so many junk foods I thought were delicious until I slowed down and discovered they were too salty, too stale, too cloying, or too bland for me. Some of them need to be paired with OTHER junk foods in order to be really enjoyable (for me, chips and popcorn taste much better with a soda alongside). This doesn't mean I'll never eat such foods again, but having experienced them in a new light, I'm unlikely to reach for them and even less likely to overeat them. Without some distracting activity paired with those foods, they just aren't that fun.
I don't think that mindful eating is a straightforward, easy solution to binge eating. Not at all. But I think it really can help lessen the grip of problematic foods. It can allow you to see that there IS hope: if your perception of a food can change via mindfulness (despite believing for years and years that your connection to that food was ironclad), then your behavior around that food can change as well. And no matter how entrenched your binge eating disorder is, there is a part of your brain that remains capable of providing insights and applying solutions to overcome it. We've got to put more stock in those parts of our brains! Mindful eating is one way of doing exactly that.