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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.