Skillet Bacon Cheeseburger with Crispy Fried Onions

In a medium skillet over medium heat, warm the oil and butter until the butter is melted. Add the onion, and cook until softened, about 5 minutes.
In a separate large skillet, preferably cast-iron, cook the bacon until about halfway done, 3 to 4 minutes. Use tongs to remove half from the skillet, set aside, and continue to cook the rest until almost crispy, then remove from the heat and drain on paper towels. Wipe out the skillet.
In a large bowl, combine the ground beef, softened onion, half-cooked bacon, and 1/4 cup of the crispy onions.
Season with salt and pepper and mix together well, then gently shape into two patties.
In the same large skillet you used for the bacon, heat 1 tablespoon of oil over medium heat, and when hot, add the patties.
Cook to your liking, 4 to 5 minutes per side for medium-well, then flip over and add the cheese. After the cheese melts, transfer the cheeseburgers to a plate.
Toast the burger buns in the skillet, then remove from the pan. Add mayo to both halves, the cooked cheeseburgers, the rest of the crispy bacon, and the remaining crispy onions. Devour.