Spread bottoms of croissants with cream cheese and mustard. Top with ham, cheese and tops of croissants. Set aside.
In shallow dish, combine eggs and half & half; salt and pepper to taste. Dip each side of sandwiches in egg to coat croissants.
In a flat skillet over medium heat, melt enough butter to coat pan. Place sandwiches on skillet; cook until golden brown on both sides and cheese is melted (about 2-3 minutes per side).