1. In a shallow dish, beat the eggs and milk together until well combined. Season with a pinch of salt and pepper.
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2. Place the bread slices in the egg mixture, turning to coat both sides evenly. Allow the bread to soak up the liquid for a few minutes.
3. In a large skillet, melt the butter over medium heat. Once the butter is melted and the skillet is hot, add the soaked bread slices and cook until golden brown on both sides, about 3-4 minutes per side.
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4. While the bread is cooking, preheat your broiler. Once the bread slices are golden brown, place a slice of Reblochon cheese on top of each slice of bread and transfer the skillet to the broiler. Cook until the cheese is melted and bubbly, about 2-3 minutes.
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