Must say I'm surprised at the response! My boyfriend and I have the EXACT same problem, all the time, and I always thought it was maybe unfair of me to expect him to pitch in - Clearly not!
OP, I agree with others who say you don't necessarily have to 'cook', but you do have to make up in other ways! I enjoy cooking, and I like making nice food for him to enjoy... but it's a bit annoying when you seem to be doing more than your fair share of things in a relationship. Cleaning up is generally the most common way of splitting up food responsibility. My boyfriend and I technically have this 'policy', but because he's so slow (and I want to say lazy), he never even thinks to actually do it unless I ask him to. Seriously, given his choice, the pots and plates will be there next morning and beyond - by which time, he'll be asking me if it's still our stuff or the other tenants. Don't get me wrong, he'll do it when I ask him (and generally not complain), but I'm so sick of always asking him! It's our joint responsibility, he should know to do certain things without needing me to be his mum, telling him exactly what to do. Sometimes I feel he should live out completely on his own for a year (not at home, and not with me), just to learn how to take responsibility for the runnings of everyday chores.
*Rant* Sorry, got carried away there... as you can tell, this issue does really bug me. And as such, I emphasise with the OP's girlfriend.
Separating meals out won't help, it'll just annoy her: if she's got to cook for herself, she's still cooking. Just learn to cook, and start making meals for a both of you a few nights of the week, so that you both have days where you get to rest from cooking. The more practice you have, the faster/better you'll become; it's not astrophysics.
why dont you just do more of the cleaning?
that's a bit mean not to eat the food you made at all...if she acts like that what does she expect?
It sounds like this problem, as others have said, maybe goes a bit deeper than just 'who cooks' - you need to sit down and talk. Tell her that you would like to cook more (if you do want to?), but that you're not that confident and you need a bit more support from her. She really should respect that...
Isn't it her job as the woman?