Egg in a hole is correct in my family,, I have heard it called a one eyed texan too. To cut the fat a little we lightly butter only one side of the bread and put the buttered side down in the pan. Also, for general use, I just tear the bread with my fingers and flip the cutout to the dog.
Also, I'll let you know how best to cook the scrapple that goes with it!
Heat a heavy frypan, but not to smoking. SLice that scrapple as thick or thin as you like it.
Butter one side of each slice. Put each slice butter side down in warmed pan. Leave it alone while you drink a cup of coffee. When the bottom is browned, flip. Have more coffee. Serve with syrup (YEAH!) or ketchup (if you must). Yum!
If you don't already know, scrapple is a local item that is made with ground pork, spices like pepper, sage, salt, onion or garlic powder and cornmeal. The cornmeal is why you butter the slices. Good eating!