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Heat a large non-stick skillet over medium heat.
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Whisk together the eggs, milk, salt and pepper.
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Add a teaspoon or so of butter to the pan, then add the egg mixture.
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Sprinkle the ham evenly over the eggs.
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As the omelet cooks, begin folding in the edges to form the omelet into a rectangle about the size of 2 slices of the bread.
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Flip and cook well on the other side.
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Transfer the omelet to a plate and cut it in half. Wipe the pan clean with a paper towel and return it to the heat.
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Lightly butter the 4 slices of bread and place 2 slices, butter side down, in the heated pan.
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Add a slice of cheese to each piece of bread, followed by half of the ham omelet and another slice of cheese.
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Top with the remaining two slices of buttered bread, butter side up.
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Cook for only a couple of minutes until the bread is golden brown, then flip and do the same for the second side.
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Cut each sandwich in half and serve immediately.