In a small bowl, combine 1/4 cup butter and mustard. Spread mixture evenly over 1 side of each bread slice.

Divide ham evenly over 3 prepared bread slices. Top each with 1 slice cheese. Cover each with remaining bread slices, buttered side down, to make a sandwich.

In a shallow dish, whisk together eggs and milk.

In a large skillet, melt remaining 1/4 cup butter over medium heat.

Dip both sides of sandwich into egg mixture, letting excess egg mixture drip off. Place sandwiches in a hot skillet, and cook for 4-5 minutes per side or until golden brown.

Sprinkle with confectioners' sugar and serve with a side of strawberry jam and potato chips, if desired. Serve immediately.