Fill a saucepan a little more than halfway with room temperature water, and place the pan over medium-high heat. Once the water reaches a rolling boil, add the eggs, lower to a simmer for 3 minutes then remove the pan from the heat. Let stand for 12 minutes (covered).
Gently tap the eggs against the counter to crack the shell in several places, then immerse in a bowl with ice water for a few minutes. This will allow ease when peeling the eggs.
Slice the eggs in half (length-wise). Gently remove the yolks either with your fingers or with a teaspoon. Place the yolks in a mixing bowl, and place the egg whites on a serving platter, sliced side up.
Using a fork, mash the yolks until they are in small pieces. Add the avocado, salsa, and lime juice into the bowl and mix until smooth.
Place the avocado filling in a plastic bag or pastry pipping bag. Pipe the filling into the egg whites so that it is slightly overflowing. To each egg, add salt, pepper, and cilantro. Serve immediately, or within 24 hours of preparation.