To a large skillet, add bacon strips and heat over MED-LOW heat. Cook until bacon is cooked to your desired crispness, then transfer bacon to a paper-towel lined plate to cool. Drain all but about a tablespoon of the bacon grease, reserving that last Tbsp in the pan.
Increase heat under the same skillet to MED heat. Add sliced onion and cook 8-10 minutes, or until golden brown. Remove onions to a plate, and turn off heat.
Divide the beef into 8 equal portions and shape into balls. On a flat surface, lay down a sheet of wax paper and top with a ball of ground beef. Top with another sheet of wax paper and use a flat bottomed pan to press the meat into 1/4-1/2 inch patties. Repeat with remaining patties.
To one of the thin patties, top with 1/8 cup cheddar cheese, a tablespoon or two of the onions, and another 1/8 cup cheese. Leave a border around the patty. Top with another thin patty, pressing the edges of the top and bottom patty together to seal well. Shape into a thick burger patty. *See recipe notes section below for a video instruction link to this part*
Double check burger to make sure there are no holes, then season well with salt and pepper.
In the same skillet, add a drizzle of olive oil and the butter and heat over MED heat. Add burgers to pan (I like to cook 2 burgers at a time to make sure I have room to flip them carefully), and cook approximately 8 minutes, until burgers are brown up the sides. Use a wide spatula and carefully flip burger to the other side and cook another 5 minutes or so, until golden brown.