Sandwiches can be cooked 4 hours ahead and cooled completely, then kept, wrapped in plastic wrap, at room temperature. Reheat in 1 layer on a baking sheet in a preheated 350 degree F oven until heated through, about 6 minutes, before cutting into triangles.
Preheat waffle iron on high until just beginning to smoke. Reduce heat to moderate and brush generously with some butter.
Spread butter on 1 side of 8 bread slices and turn slices over. Top 4 slices with 1 slice ham and 1 slice cheese, folding in any overhang, then top with remaining 4 buttered bread slices, buttered sides up. Cook sandwiches in batches (number of batches will depend on size of your waffle maker) until bread is golden and crisp, 4 to 6 minutes.
Assemble and cook 4 more sandwiches in same manner.
Just before serving, cut each sandwich into 4 triangles.