Finely chop the cabbage. Heat a frying pan with oil. Break the eggs into a separate bowl.
Place finely chopped cabbage in a heated frying pan, add salt, stir and cover with a lid. Leave for 10-15 minutes, stirring occasionally.
Mix the eggs in a bowl until smooth, add milk to them, add salt and mix again. Stir the stewed cabbage again and carefully pour the egg mixture into it, then cover again and leave for 10 minutes.
Remove the pan from the stove, transfer the omelette to a plate and serve.
Garnish the finished dish with fresh herbs, such as dill.