Preheat your Blackstone griddle to high heat.
On one side of the griddle add the olive oil and butter, and let it heat for about a minute.
Add the onions to the griddle, and sprinkle with salt and pepper. Use a spatula to toss the onions frequently to prevent sticking and ensure even cooking.
Continue cooking the onions on the griddle for about 20-25 minutes, or until they are soft and caramelized to your liking.
Divide the ground beef into 4 equal portions and form into balls.
Season each ball with salt and pepper on both sides.
Place a ball onto the griddle and smash it down with a spatula until it's about ¼ inch thick.
Repeat with the remaining balls and leave them on the griddle for about 2-3 minutes until the edges start to brown and the burgers release from the griddle.
Flip each burger and add a slice of American cheese on top.
Let the cheese melt for about 30 seconds.
While the cheese is melting, butter the brioche buns and place them on the griddle until they are toasted.
Assemble the burgers with the buns and your desired condiments.