A cat who is biting when hungry isn't 'hunger biting' (which would be more along the lines of actually eating you, lol), but rather biting out of frustration and lack of impulse control.
The boys used to do this when they were very little, but IMO it's very rude and does NOT get rewarded with food! Ditto for any other inappropriate behaviors around dinner - I taught the boys to sit for their dinner instead. It took a bit of work, but once they knew what was expected (and that being naughty meant waiting for dinner) they caught on pretty quickly.
The basic steps are to teach 'sit' (look up a youtube video, works the same for cats as it does for dogs. Easy peasy.), stop rewarding the behavior you don't want to see, and ask for the behavior you do want to see - rewarding that.
To stop rewarding the biting behavior you have to not react to it as though it hurts (even if it does). Use a marker word, so they can figure out what you're reacting to (I use 'Uh uh') and then remove yourself from the room. So, if you were preparing their food and kitty bites you you'd say "Uh uh!" and then walk off, taking the half-prepared food with you. You may need to go into the bathroom or something to avoid further frustration behaviors. Go back in about 3-5 seconds (so...walk to the bathroom, shut the door, then immediately come back out and go about preparing the food again), and give the kitty another chance right away. Repeating your sound and moving away if you receive another chomp. It's crucial to remain calm! If you get upset or yell or anything else it could become a game and you could end up with a much bigger issue.
Most cats will respond with confusion the first few times this happens, giving you a break of good behavior (or at least not unacceptable behavior) to allow you time to finish preparing the food, then you can set it down before they have a chance to be naughty again.
Some cats will become MORE frustrated, since they don't understand why you're going away and they still WANT the dinner. Those cats need to be given another task to do while you're working on the food. I'd suggest teaching them to sit on a stool nearby, but out of biting range.
To teach this get a stool, how high doesn't matter, a lot of very tiny high value treats (I use dehydrated chicken crumbled into cat-bite sized pieces), and patience. lol
Lure the kitty up onto the stool with a bite of chicken treat. When they're on the stool put another treat right between their paws, then turn away and start to prepare the food. You'll need to reward every 5 seconds or so when you start out, to get them to the point where they figure out what's going on. If your cat keeps jumping down you're not rewarding often enough. If they do jump down, lure them back to the stool and reward.
If you find that as soon as they've eaten the first treat they're immediately jumping down you need to up the rate of reinforcement - aka MORE COOKIES
With young kittens (impatient) or older cats with no impulse control the first step might literally be getting them onto the stool, then giving them 5-10 treats one after the other on the stool. Just waiting long enough between presentations to let them swallow the previous treat. Once they've gotten the idea that them being on the stool means goodies start spacing the treats out a little more, 1-2 seconds in between, then work up until you can progress. The key is to take VERY small steps to the goal so the cat always is interested and willing to 'play' with you. It has to be fun, or they'll go back to chomping!
Once you're at 5 second intervals work on 'doing something' in between rewards. pick up a spoon, then set it down. Get the can of cat food, then put it on the counter, etc. Keep your steps tiny and reinforce the cat for staying on the stool. If they jump down simply guide them back to the stool (don't just pick them up and set them on the stool, they'll never figure it out on their own if you do it for them.). Again, if they're constantly jumping down reduce the time in between treats, and maybe move the stool a bit closer to your workspace, it should be about one big step away.
Continue practicing daily until they'll sit nicely on the stool while you prepare their dinner with one or two treats as motivation. The key is that, once they've got a solid handle on the process, you need to vary the length of time between treats. They can't know when it's coming or they'll get lazy and bored of the game. Like if you always knew when your favorite sports team would score - if they only ever scored in the third period would you keep watching the whole game after a full year of that? Boring. Predictable. The fun is in the NOT knowing.
I'm teaching Muffin a more advanced version of this, so we can teach him to 'go to his place' when he's being a brat and can then reward him for making a good choice, rather than having to fight with him about chasing his sisters....Maybe I'll make a 'how to' video of 'go to your place' for kitties....