Except mine don't.
I made a broccoli tree by wedging broccoli florets in the branches of a shrub in their Run. A few hours later, DH went out to measure up for a ramp to go over their ladder, and reported back that there was broccoli all over the floor of the run. Seems they prefer to kick it about rather than eat it.
They do, however, go mad for cooked rice and cooked pasta.