Quavers are very nice. I sympathise.
At 11 months I'm guessing he's not old enough to actually ask for them - or is he? He may also not be old enough to understand if you explain they are run out. At least you're able to get a few spoonfuls of something good in.
What happens if you crunch up quavers and sprinkle them on stuff as an intermediary step?
You could sprinkle them on broccoli as a kind of broccoli cheesy thing - if you leave some slightly larger pieces he will recognise what it is. Or use them as dippers for other foods (before they get too soggy). Use them to dip into mashed vegetables so he has to eat them with something. Hmmm. It's not easy but I would probably just not have them in the house to remove temptation and if he's hungry he will eat something. You could change location of meals for a bit to break assocation.
The ingredients list of quavers isn't great - especially for a baby under 12 months. MSG and sodium levels would inspire me to go cold turkey. MSG is quite an 'addictive' ingredient so I can see where his craving comes from. I found this quote in an article about MSG you might find interesting:
Babies have very basic taste buds: it's believed that mother's milk offers two taste enhancements - sugar (as lactose) and umami (as glutamate) in the hope that one or other will get the little blighters drinking. Which means mothers' milk and a packet of cheese'n'onion crisps have rather more in common than you'd think.Good Luck.
One more thought. Are you in the UK? The 'Goodies' company who sell baby food in most major supermarkets make 'crisps' that are organic and contain ingredients like baked corn, organic oil, organic cheese powder. They aren't as healthy as your broccoli florets but they are a big step up on quavers. They make sweetcorn rings and cheese puffs and carrot stix which aren't a million miles from quavers in texture. They are officially 12 months+.
http://www.goodies.uk.com/our_foods/our_range.asp?p=2