Spread cream cheese on two slices of bread. Layer 2 slices of ham, 2 tablespoons of pineapple, and one slice of cheese over the cream cheese. Then top each sandwich with one more slice of bread. Cut off crusts.

In a shallow bowl, whisk together eggs, milk and sugar. Briefly dip both sides of sandwiches in egg mixture.

Heat butter and oil in a large skillet over medium heat. Place sandwiches in skillet, and fry on each side until golden brown and cheese is melted, about 5 minutes per side. Drain on paper towels and cool for 3 minutes before serving.