In a bowl, whisk together the eggs, salt, and pepper until well combined.
Heat a non-stick skillet over medium heat. Add the butter and let it melt, swirling to coat the pan.
Pour the egg mixture into the pan. Let it cook undisturbed for about 1-2 minutes, until the edges start to set.
Sprinkle the crab meat, cheese, and herbs evenly over one half of the omelette. Optionally, add a light squeeze of lemon juice for more flavor.
Using a spatula, gently fold the other half of the omelette over the fillings. Cook for another 1-2 minutes, until the cheese melts and the eggs are fully set.
Carefully slide the omelette onto a plate. Garnish with avocado slices, sour cream, and more herbs if desired, and serve immediately.
