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 will 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 take on a brown coloring.
After about 20 minutes, remove the eggs, bring them inside, and let them rest. Serve them fresh, or keep them in the refrigerator for up to three days.
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.