4 tablespoons butter
1 1/2 tablespoons flour
1 cup whole milk
Salt and freshly ground pepper
A pinch of ground or grated nutmeg (for people's sammies only)
2 teaspoons Dijon mustard (for people's sammies only)
8 slices sandwich bread
8 slices deli ham
8 slices Gruyère or Swiss cheese
In a small saucepan, melt 2 tablespoons butter over medium heat. Whisk in the flour and cook for 1 minute. Whisk in the milk until thickened, about 5 minutes. Season the sauce with salt to taste. Reserve a quarter of the sauce for the dog's sammie. Season the remaining sauce with the pepper and nutmeg and whisk in the mustard.
Spread one side each of six bread slices with the people's sauce. Use to make three sammies with two slices each of ham and cheese. Spread the remaining two bread slices with the dog's sauce and then assemble the sammie using the remaining ham and cheese; keep separate.
In a large skillet, melt the remaining 2 tablespoons butter over medium-low heat. Add the sammies and cook, turning once, until golden on both sides, about 4 minutes total. Chop up the pup's sammie and let cool, but eat yours hot.