Slice each 4-bun set in half through the middle and open up like a sandwich. For each sandwich, place one slice of cheese on the bottom bun and top with ham. Place tops on each of the 4 sandwiches.
Cooking one sandwich at a time, place in centre of waffle iron and cook for 2-3 minutes while pressing down firmly to flatten and toast sandwich. Remove and place each cooked sandwich on a sheet pan.
Prepare sauce: Melt ¼ cup (1/2 stick) of butter in a small sauce pot over medium heat. Add the flour and cook for 2 minutes while constantly stirring. Slowly whisk in the milk and add the nutmeg. Increase the heat to medium-high and bring to a boil. Whisk constantly while the sauce thickens. Cook for about 3-4 minutes while stirring and add salt & pepper.
Spread approximately 2 tablespoons of béchamel on top of each sandwich and top with grated gruyere cheese. Place sandwiches under broiler for 45-60 seconds until the cheese is golden brown and bubbly. Top with grated pecorino and chives.