Butter both sides of each slice of bread with 2 tablespoons of the butter. In a saute pan, heat the remaining butter. When the butter has melted, crack each egg into the pan (make sure you crack the eggs about 2 inches away from each other). Season the eggs with salt and pepper. Pan-fry the eggs for about 2 to 3 minutes or until the white is firm and the yolk is still runny. To build the sandwich, divide the cheese between four slices of buttered bread. Season both sides of each tomato slice with salt and pepper. Place two slices of tomato on top of each piece of cheese. Divide the ham in four potions and place on top of the tomatoes. Place the fried eggs on top of the ham and place the remaining buttered bread on top of each fourth. Heat the saute pan. When the pan is hot, carefully add the sandwiches in the hot pan. Pan-fry the sandwiches for 2 to 3 minutes on each side or until each side of the sandwich is golden brown. Serve warm.