I looooove to peel potatoes & carrots. It's odd but true I would probably be content to be the guy on KP peeling a bag of spuds.
Mind you I like to use a Japanese veggie peeler cuz' those US ones are very bizarre & should be banished forever from kitchens.
So, basically what I sometimes do is just peel the entire carrots down to the nib & have a whole bowlful of shavings to add to the salad. Of course I think it'll initially freak some people out into thinking you're making a compost salad but personally I think it's purty & easier to eat than grated carrots. So there ya go!
PS. My kids love help peeling carrots this way since they end up doing it anyway.