I can! My sister-in-law mentioned over the holidays that it's possible to peel a hard-boiled egg without the tedious task of peeling off broken pieces of shell. She had seen a video where they had pinched off some of the shell on either end of the egg and then blew on one end until it popped out the other. Admittedly, I didn't believe her. So I had to see it for myself. I googled "how to peel a hard-boiled egg without peeling" and found Tim Ferriss' instructional video. Not only is he handsome enough to watch, he demonstrated how easy it was to perform the aforementioned task. In the video, he shares the following tips:

1. Slow boil the eggs with about 2 inches of water above them for about 12 minutes.
2. Cool the eggs in ice water and add a teaspoon of baking soda. This lowers the pH balance which thereby reduces adhering. (I didn't have any on hand but it still worked!)
3. Crack one end of the egg by gently tapping it on a hard surface and pinch the end to remove a bit of the shell. Repeat on the other end.
4. Hold the egg securely in one hand, pointy side up, and bring your hand to your mouth. Your finger and thumb will form a circle that should fit around your lips to create a bit of a seal.
5. Blow until the egg comes out of the other end. Don't forget to catch it.

NB. (update) - Some readers have expressed concern about the unhygienic nature of doing this. I do NOT endorse this as something you should do if you plan on serving the eggs to anyone other than yourself. Simply cooling the eggs in ice water will make it easier to peel by hand and safe to serve to others, assuming you have washed your hands.

Here's what I had left after attempting this for the first time:

I've included the link to the Tim Ferriss video below. I told you he's cute.

You can also learn why you shouldn't use farm fresh eggs when hard-boiling from Ontario egg farmer Diana Schenk on eggfarmersontario.ca.