I'm sure we've all witnessed our beardies repeatedly trying to get a piece of squash, carrot, or apple in their mouth with little success. Maybe they'll get a couple pieces in, but ultimately it seems like they end up eating less of the good stuff in a sitting because it's too difficult.
Enter the vegetable peeler.
I've found that if instead of chopping vegetables, using a vegetable peeler to shred the vegetables into long fettuccine shaped ribbons that you shape like a mound of pasta in their cage makes things far easier.
Another helpful way to prepare things like squash is to grate them using the large holes on a box grater. This produces a similar effect (worm shapes) in slightly different form.