Everyone has their favorite recipe for boiled/deviled eggs, but this isn't about that. This is about technique, not taste. What I find really annoying is that when you fill them, they get top heavy, and unless you want to put them into a fancy holder, the tendency is to for them to fall over.
Well, no more. If you add a few hours of resting time into your preparation planning, you can have very unusual yet stable eggs for your guests. What's fun is to see if anyone even notices...
one dozen eggs (at least a week old makes for better peeling)
Place the eggs into a pot and cover with cold water. Over high heat, bring to a boil. Cover, reduce heat and let lightly boil covered for 10 minutes. When time has elapsed, carry pot to sink and run cold water into pot to displace the hot water and cool the eggs.
Finally, I put the eggs into water and ice until cool. This not only cools them faster, but makes them easier to peel.
Peel the eggs carefully, removing all the shell but leaving the surface unblemished. Place the peeled eggs on a plate with a raised edge, so they don't skitter away. I leave them wet from the peeling process so that they can easily move around a bit.
Next, use a sturdy flat pan of some type or an inverted plate to cover the eggs. Weigh down the top plate with containers equaling 4-5 lbs. or so, placing them on top of the upper plate and checking to see that the weight is evenly distributed.
Over the space of a few hours, the matrix of the cooked egg whites will relax and allow the steady pressure to change the shape of the egg.
Give it 5 or 6 hours. Once you remove them from the fridge, they will be flat on both sides - just enough to keep them stable. Now when you prepare your eggs, deviled or otherwise, they will sit nicely and not roll or fall. Let everyone else figure out how you did it...