Bulimic cat? Not trying to be funny.

I have two cats who are sisters, that I raised from about 5 wks of age. They are now almost six years old and in great health. They are strictly indoor cats. One is spayed, the other is not. The one that is not spayed (Spooky), is the one I have the question about: For the last couple years, whenever her food bowl gets somewhat low, she will gorge on what's left until she throws up. Likewise when I refill the bowl. She will eat until she throws it back up. Then she will follow me around the house waiting to be fed again, even though her bowl still has plenty in it. They both eat from the same bowl, and Shadow doesn't do this, except on the rare occasion she has a hairball. I've tried changing the diet...no avail. I've had cats my entire life but never one like this one. They have never gone without--twice daily I freshen their food and water. Help?

Welcome to the Weird Cat World.
   
Get Spooky spayed. It can only help.
   
Try giving them separate dishes & eating areas. It may change her behavior.
   
Limit the food, don't feed on demand. Feed a finite amount twice a day. This will also keep them from getting fat.
   
Average-sized cats only need to eat one 6-oz can of food per day in 2 meals. For dry food, subsitute 1/8 cup of kibble for half a can of food.
   
One meal at least should be canned. Ad extra water so the food is the consistency of stew. That way, she'll have to almost drink it. She can't bolt it if it's more liquid, she'll have to lap it.
   
Spread the food out on a medium-sized plate so she has to swallow what she has in her mouth before she gets to the next bit of food. I use this technique to slow down the eating speed of my cats that bolt their food.
   
She's swallowing air along with the food, and she's not chewing the kibble.