I have a cole slaw recipe that calls for shredded onion, celery, red bell pepper, and carrot. What cut is this? Do I need a food processor for this. Can I use a box grater?
As Karl said below, I usually use the "slicer" portion on a box grater for onions. I cut the onion in half and then each half again so I have a short side of the "onion slice side" that I can then run against the slicer on the grater (if I don't feel like hand-slicing or using my mandoline). I can then chop those slices up as needed. But...I have used the larger holes on the box grater and that doesn't turn the onion to mush as much.
I seem to have overlooked the celery in the OP's initial post. I think I'd just finely dice that item, as shredding it seems virtually impossible!
Shredding is a kind of slicing: typically very thin, but also somewhat short. If you don't have a food processor or mandoline, you could do this with a knife, which is, after all, how shredding was done for generations before the invention of those nifty tools.
The carrot will generally shred well on a box grater. If you remove the outer strings of the celery (it's kinda like stringing string beans - you snap the root end but not completely, and try to pull up along the outside strings), the celery might work well shredded, though you can always just dice celery for cole slaw.
The onion and pepper are wetter than the celery and carrot, and thus more likely to get mush on the shredding sides of the box grater. Many box graters have a slicing option on one of the short sides, a primitive kind of mandoline. That would be an option.
But in the end, you can always finely slice and then cut across for shorter lengths.