Pre-heat a large skillet or griddle over high heat for 5 minutes.
While the pan is preheating, spread butter on one side of each slice of bread.
Measure out about a 4-ounce portion of ground beef and form it into a round or square patty that's around 1/4 inch thick and about 5 inches in diameter. I like to form each patty on parchment paper so they're easier to transfer to the hot surface. Season the top side of your burger patty with salt and, optionally, black pepper.
Place your ground beef patty on the hot skillet or griddle. Season the exposed meat with salt and/or pepper. Cook for 4 minutes and flip the patty. Once flipped, cook 3 more minutes.
When your burger is finished cooking, remove it to a plate briefly while you toast the bread.
Reduce the heat in the pan to medium-low. Add your two slices of bread, butter side down, into the pan or griddle. Top each slice of bread with one slice of American cheese.
Toast the bread for 1 minute and then check to see how browned the underside is. Continue toasting for 30 seconds at a time until the underside starts to look golden brown. Move the cooked burger patty to the top of one slice of bread and cheese, and then flip the other piece of bread on top of the burger patty, forming a sandwich. Continue toasting and flipping the sandwich until both sides of the bread are nicely golden brown.
Remove the completed Chester to a cooling rack to rest for a couple of minutes. If you place it directly on a plate, the bottom of the bread will steam and become soggy. Allowing the burger to rest on a cooling rack allows air to circulate and keeps the bread from becoming soggy.
Serve and enjoy.