Crack the eggs into a bowl and beat them really well, then add the milk, parsley and mustard powder, season with salt and pepper, and mix well. Throw in the ham and Cheddar.
Heat the butter in an ovenproof skillet over fairly high heat until it’s fully melted and the pan is very hot. Pour in the egg mixture, pushing the egg away from the sides of the pan using a heatproof spatula. Immediately turn the heat down to medium and let the omelet cook slowly until the bottom half of the omelet is set, about 3 minutes
If you want to fold your omelet, use the spatula to flip 1 side of the omelet over the other to form a half-circle and continue to cook until the omelet is set, about 3 minutes more. If you want to leave your omelet flat, slide the skillet under a preheated broiler until the top of the omelet is set, about 3 minutes.
Once the omelet is cooked, serve it immediately, whether folded or flat.