Well I thought I was reading my own Diary. My youngest son did this same thing at around the same age (maybe earlier). He is a very anxious kid. I believe it was one small way for him to control his "situation".
Everyone thinks you have to squash him down and make him cut it out. But that really doesn't solve the problem - and it's "real" to him. At that age (as someone pointed out) they do not understand "eat this first and then you can have more" - at least mine didn't. And trying to fool him by putting the package away won't work if your kid has a brain. It never worked for mine (just made him madder).
No one will like my answer (based on what I've read), but we fought with my little guy for weeks, screaming and yelling first thing in the morning (with mine it was mostly about cereal for some reason, but he did it with other stuff too. It's the morning screaming matches I remember most). I worried endlessly and researched on the web about food issues and hoarding and anger issues and I thought we were going to have to take him to a shrink.
And then I did the unthinkable. I just gave him as much as he wanted. Bowls would be overflowing with cereal (or whatever). I even let him have the box (heaven forbid!!!)
Here's what I believe in hindsight: My poor little guy was so stressed out about the world around him this was just one small way he could have control. And I "allowed" him to have that control. Don't you know, things started to get easier until one day (and I can't tell you how long it took - selective memory I guess) he just let me pour his cereal for him and never asked for more. Food has not been an issue since and he is actually the better eater out of my two boys - lots of fruits and veggies and variety.
I think if you fight with him on this all it will do will make everyone miserable and him more anxious. The hardest part for me was that there was a lot of waste. But I finally said the mental health of my family was worth a few extra cups of rice krispies.
Your situation is harder because you have twins. If it would be possible at all to let your "eater" have as much as he thinks he wants I would do it. Contrary to all the advice you have been given. I noticed that all the posts I read were from people that had never actually gone through this. I have. It ain't fun, but it will end.
My guy is still pretty anxious, but I have learned that these "tantrums" are signals, not some evil plot to put one over on me (OK, sometimes they are evil plots, but not the majority of the time). Patience is what's needed (and oh my it's hard) and try to see the world from his point of view: "Wow this big world is pretty friggin' scary and not only that, I have a twin brother I have to deal with and I also have a Mom who is worried about me and (probably) a Dad who doesn't understand why I act the way I do and maybe if I can just control this one little thing I'll feel just a touch better...."
It won't turn into an eating disorder, I promise. My son is still a challenge in many ways, but he is so passionate and complex and incredibly smart I wouldn't trade him for anything. He has made me learn a lot about myself by learning about and trying to understand him.
I really wish you luck. Go with your gut. It's not our job to cut our kids down if they express themselves or try to "tell" us they are having trouble. It's to try to understand and support them as much as we can. I know this is easier said than done, trust me I lose it more often than I'd like to admit. But my son knows that he can come to me if he's feeling freaked out and I'll tell him how much I love him no matter what. You don't get that when you throw him in a time out.