Start heating your broiler, grill or toaster oven to its highest setting.
Melt the butter in a saucepan, add the onion and cook until softened but don't let it brown. Add the cheese and mustard (and beer, if desired: see tips), lower the heat, and stir until the cheese has melted.
In a separate bowl, mix the eggs and the milk. Then add to above when the cheese has melted. Stir it continuously for about 5 minutes (a whisk is ideal, if you have one.) You want this sauce to thicken without letting the egg congeal. Then remove from the heat, and season with salt and pepper.
Toast 4 slices of bread on both sides. Spread the cheese sauce on one side of each piece of toast, and place the toast sauce side up under the grill / broiler, and grill until bubbling and golden -- it won't take long, so watch it closely, as it will reach the point where one moment it will be almost there, and if you take a quick second to do something else and come right back, you will find it burnt in several spots!
If you have sour cream on hand, it would be nice instead of the milk.If you have any beer on hand, and want an excuse to open a bottle, add 3 tablespoons of beer or stout when you are adding the mustard -- after all, you can always drink the rest of the beer with your meal.For mustard, use any kind of mustard -- such as Dijon -- but yellow hot-dog mustard may not "cut the mustard" here. But you can try.This recipe is easy doubled or tripled.