Use 2 tablespoons of the butter to spread over one side of each slice of bread. On three of the slices, spread a layer of Dijon mustard over the butter, and top each with 4 slices of ham. On the other three, spread mayonnaise, and top each one with 2 slices of Swiss cheese. Press ham and cheese sides of sandwiches together.
In a flat bottomed dish, whisk together the flour, baking powder, salt, eggs, and water until blended. Set aside.
Heat remaining butter and vegetable oil in a large skillet over medium heat. Dip both sides of each sandwich in the egg mixture, and fry in the oil and butter until browned, flipping to brown on each side.