Begin by adding the eggs to a large pot of cool water. Bring to boil. Once boiling, cover and removed from the heat. Keep covered for 13 minutes. During this time, fill a large bowl with water and add about a cup of ice.
Remove the eggs with a slotted spoon and place them into the ice water to quickly cool.
Take an egg out, and gently tap the egg on the counter, just lightly cracking the shell. Carefully remove the shell from the egg. It should peel right off. Repeat with the other egg.
Next, with a long and sharp knife, slice the egg in half, lengthwise. To another bowl, add in the diced avocado, and season with salt. Add the cooked egg yolks from each of the eggs, and place the cooked egg whites onto a plate.
Mash the avocado and egg yolks until you have a smooth mixture.
Spoon the avocado mixture into each egg. Shower the eggs with the pico de gallo, and serve.