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Spread all the bread with dijon mustard. Top 4 pieces of bread with ham and Swiss cheese. Top with remaining 4 slices of bread.
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In a small bowl, whisk together eggs and milk.
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Heat 1 tablespoon of butter over medium heat until melted. Dip a sandwich into the egg mixture, making sure to coat it well, and then place in the hot pan. Cook until golden brown, flip, and cook until that side is golden brown.
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Top with powdered sugar and serve with strawberry jam on the side.