How To: Make Betty's "square deal" hamburger recipe

Everybody loves burgers and everybody loves sandwiches - so why not combine them? In this tutorial, Betty makes square shaped sandwich burgers from scratch. This recipe is not difficult to make and is incredibly tasty. But, make sure you remember the napkins because this dish sure is messy!
You Will Need:
*1 pound lean ground beef
*1 egg, well-beaten
*1 teaspoon salt
*1/4 teaspoon garlic powder
*ground black pepper, to taste
*1 tablespoon olive oil
*1/2 of a medium white onion, finely chopped
*1 tablespoon butter or margarine
*2 slices American cheese for each burger
*2 tablespoons softened butter
*mayonnaise, to taste
*2 slices bread for each burger(any type)

Step 1:
In a large mixing bowl, beat one egg.
Add 1 pound of lean ground beef, 1 teaspoon salt, 1/4 teaspoon garlic powder, and a dash of ground black pepper.
Use an electric mixer to mix these ingredients until the mixture is fine.

For my burgers, I separated the ground beef mixture into 3 equally-sized portions. I used one portion to form a hamburger patty in the shape of one of my bread slices (a little larger, to allow for shrinking as it cooks).

Step 2:
Place 1 tablespoon olive oil in a medium skillet, and add hamburger patty. Fry until done all the way through and crisp on the outside.
Meanwhile, spread softened butter on 1 side of each of 2 slices of bread. Toast the buttered side in a skillet, and return it to your work space, toasted side up.
Also, while your hamburger is frying, saute 1/2 finely chopped onion in 1 tablespoon butter, until soft and clear.

Step 3:
When your hamburger is cooked, begin assembling your sandwich burger. On top of each of the 2 slices of toasted bread, spread mayonnaise, to taste. Then, on each of the 2 slices of bread place 1 slice of American cheese on top of the mayonnaise. Next, place sauteed onion of each of the two American cheese slices, as much as desired.
Place the fried hamburger patty on top of the sauteed onion on one