Crack the eggs into a medium mixing bowl. Add the milk, salt, and black pepper. Whisk until the mixture is smooth and slightly frothy. This helps create a soft, fluffy omelet.

Heat a nonstick frying pan over medium heat and add half the butter. Once melted, add the chopped onion and cook for 1–2 minutes until softened. Add the spinach and cook for another 1–2 minutes until wilted. Transfer the vegetables to a small plate.

Add the remaining butter to the same pan and let it melt. Pour in half of the egg mixture, tilting the pan gently so the eggs spread evenly. Cook over medium-low heat until the edges begin to set while the center remains slightly soft.

Spread half of the cooked spinach and onion mixture over one side of the omelet. Sprinkle half of the shredded cheddar cheese on top. Let it cook for another 30–60 seconds until the cheese begins to melt.

Gently fold the empty half of the omelet over the filling using a silicone spatula. Cook for another 30 seconds until the cheese is melted and the eggs are fully set but still tender. Carefully transfer to a serving plate.

Repeat the same process with the remaining egg mixture, spinach, onion, and cheese. Garnish with fresh parsley if desired and serve immediately while warm.