Crack the eggs into a bowl and whisk with either the water or soy milk. Add the sea salt.
Heat a small sauté or omelet pan over medium heat, then add the oil to the pan. Once the oil is hot (be careful not to allow it to smoke), pour in the eggs. Using a flexible spatula, lift the edge of the egg from the side of the pan and allow the wet egg to roll to the bottom of the pan.
When the eggs are firm, lay fresh herbs and sliced avocado on one half of the omelet. Turn off heat and fold the egg over to serve. Top with black pepper to taste.