I just tried this technique over the last few days but only one of my cookies came out. For the others, the icing broke from the pressure of the stamp. When I tried pressing it less hard, large portions of the stamp didn't come out. I dried my icing overnight - it had at least 16 hours of drying time. Do you think I need to let it dry longer?
No, you don't need to dry it longer if the icing was indeed dry all the way through. Was the underlying icing soft when you broke through? If so, then dry more. But if you dry the cookie too long, the icing can be a little more prone to breaking.
I think the issue probably has more to do with how much pressure you're applying and/or how you're inking the stamp, and possibly your icing recipe. It takes a while to get the hang of how much pressure to apply to each stamp, so I always practice on paper a bit with a new stamp before I move directly onto the cookie. I actually press pretty darn hard (on icing that is dry all the way through), and the cracking of icing is minimal (maybe once every 20 or more cookies). You also have to be careful to press all over the surface of the stamp, but more so in the center of the cookie where the icing tends to sink and dry lower, to be sure the stamp makes contact there. Also, be sure you start with a very even application of food coloring to the stamp - I think the best way to ensure this is by inking with an uninked foam pad (just moist with food coloring) versus painting the coloring on the stamp. Hope this helps.