D.K.
He may be using you for a pacifier. At 11 mos he should not need to wake to eat, but he is waking and using you to get himself back to sleep. Do not nurse him when he wakes, rub his back if you have to but try not to nurse him back to sleep.
It won't be easy but if you want some peace, he should be able to go all night without needing food. Babies wake, several times during the night, that is normal, the difference is he is used to waking up and you puttting him back to sleep at the breast.
The year mark is a great time to wean him all together and just my suggestion for you to get some rest. He doesn't need breast milk any longer at the year mark for nutrition as he should be getting most of what he needs from solids now.
Try just not nursing him back to sleep, it may be tough a few nights but giving him the gift of learning to fall back to sleep on his own will help you both big time! It is a gift to break these bad habits now, instead of later. He could also be teething and using nursing to soothe his gums, try seeing if he is and try motrin before bedtime. That may help you encourage him to sleep all night.