Whisk together eggs, milk, salt and pepper, to taste, in a small bowl. Melt 1 tbsp (15 mL) butter or margarine in a skillet over medium low heat. Add egg mixture and cook, stirring, until just set, Remove eggs from heat. Divide scrambled eggs evenly between 4 slices of bread and top with one slice of cheese and one slice of ham. Top each sandwich with a second slice of bread. Spread remaining butter or margarine on the outside of each sandwich. Heat a skillet over medium heat. Cook sandwiches, in batches if necessary, until golden brown on both sides and cheese is melted.
Tip: If you have a panini grill, cook sandwiches with lid closed until bread is golden brown and cheese is melted.