Preheat your oven to 375°F (190°C).

In a medium bowl, beat the eggs with a pinch of salt and the milk until well combined.

Dip each slice of bread into the egg mixture, ensuring both sides are coated.

Place 3 slices of the dipped bread on a baking sheet lined with parchment paper.

Top each slice with grated mozzarella cheese, a slice of cheddar cheese, and a slice of ham.

Cover with the remaining 3 slices of bread to form sandwiches.

Pour any remaining egg mixture over the top of the sandwiches and sprinkle with any extra mozzarella cheese.

Bake in the preheated oven for 10-12 minutes, or until the sandwiches are golden brown and the cheese is melted.

Remove from the oven and let cool slightly before serving.