Prepare the Egg Mixture: In a shallow bowl, whisk together the egg, milk, and a pinch of salt until fully combined. This mixture will soak into the bread, giving it a soft, custardy texture once cooked.
Assemble the Sandwich: Spread a thin layer of mayonnaise on one side of each slice of bread. Layer cheese slices and ham or turkey between two pieces of bread, ensuring the cheese is evenly distributed. Press gently to keep the sandwich together.
Heat the Pan: Place a skillet or nonstick pan over medium heat. Add 1 tbsp butter and let it melt, swirling to coat the pan evenly.
Dip and Cook: Dip the assembled sandwich into the egg mixture, coating both sides evenly but not letting it soak too long or it will get soggy. Place the sandwich in the hot pan. Cook for 3–4 minutes per side until golden brown and the cheese is melted. Adjust heat as needed to prevent burning.
Serve Warm: Transfer the sandwich to a cutting board. Let it sit for a minute, then slice diagonally. Serve immediately for best texture and flavor.
