Melt butter and sauté capsicum and mushrooms for 5 minutes. Remove from heat.
Meanwhile, lightly beat the eggs with milk, sea salt and pepper together with a fork. Pour the egg mixture immediately into the pan and cook, ensuring the egg is being cooked evenly on the pan. When the underside is golden, lower the heat. Scatter the grated cheese, herbs and diced capsicum and mushroom. Arrange the ham on top.
Cook for a further 30 seconds then slide the omelette from the pan onto a plate, ensuring the omelette folds over itself. Rub in butter and sprinkle with remaining cheese and herbs. Serve immediately.