In a mixing bowl, crack the large eggs and add the milk, fish sauce, salt, and black pepper. Whisk vigorously until frothy.

Gently fold in the cooked crab meat, green onions, and cilantro into the egg mixture.

Heat a non-stick skillet over medium heat and add vegetable oil.

Pour half of the egg mixture into the skillet and cook until the edges set and the base is golden brown.

Fold the omelette in half and cook for an additional 1-2 minutes, then transfer to a plate.

Repeat the cooking process for the second omelette with the remaining egg mixture.

Serve warm garnished with lime wedges.