Place the two eggs next to each other at the bottom of a saucepan and pour cold water over them until they are submerged two to three centimeters. At the same time, prepare a bowl with cold water and ice cubes for later.
Place the pan on medium-high heat and bring the water to a boil. Reduce the heat immediately once the water boils, so it simmers gently. Cook the eggs for five to six minutes for a soft yolk, seven to eight minutes for a runny yolk, or nine to eleven minutes for a hard-boiled egg.
After the desired cooking time, remove the eggs from the pan and place them directly in the ice bath for five minutes to cool. Tap the eggs on the counter, remove the shell, and cut them lengthwise in half. Remove the flesh from the half avocado and cut it into slices or chunks.
Distribute the avocado and halved eggs over a plate. Sprinkle the sea salt and freshly ground black pepper evenly over them and serve immediately.