Boil the eggs indoors like you normally would. I cook mine in the instant pot for 7 minutes. I find the eggs cooked in the Instant Pot peel a lot easier.
Let cool and peel the eggs.
Smoke the Eggs
Set up your grill for indirect heat. For a gas grill, turn off the burners in the middle of the grill. For a Kamado-style grill, add a plate setter.
Bring the temperature of the grill to about 200-225 degrees and add the wood (or wood chips). For a gas grill, use a smoker box.
Make sure that the grill is smoking nicely before adding the hard boiled eggs.
Place the peeled hard boiled eggs in a disposable aluminum pan and place it on the grill. The goal is not to cook the eggs more, but rather to give them a good smoke. You will notice the outside of the eggs takes on a brown coloring.
After about 20 minutes, remove the eggs, bring them inside, and let them rest.
Notes
For a lighter smoked flavor, smoke the eggs with the shells ON. Only a little bit of the smoke will penetrate the shell.For a medium smoke, crack the egg shells, but do not remove them.