For the caramelized onions: Heat the oil in a large cast-iron pan over medium heat, add the onions and cook, stirring occasionally, until soft and caramelized, about 10 minutes. Season with salt and pepper to taste. Transfer to one side of a rimmed baking sheet and set aside. Reserve the cast-iron pan.
For the burgers: Place the buns cut-side up on the other side of the rimmed baking sheet, brush the cut sides with some canola oil and sprinkle with salt and pepper. Toast in the oven until golden brown, 4 to 5 minutes.
Divide the meat into 8 equal portions (about 3 ounces each). Shape each portion with your hands into a thin patty and place on another baking sheet. Places 2 slices of cheese each in the center of 4 of the patties. Place the remaining patties on top of the cheese. Pinch together the edges of both patties to seal. Sprinkle both sides of each burger with salt and pepper.
Heat the same cast-iron pan over high heat. Add the canola oil and let heat until it begins to shimmer. Put the burgers in the pan and cook, flipping once, until golden brown on both sides and cooked to medium doneness, about 8 minutes total.
Carefully add a splash of water and immediately cover tightly with a lid. Cook about 1 minute longer (the steam will ensure the cheese in the center melts completely).
Place the burgers on the bottom buns and top with the ketchup, sliced pickles, caramelized onions and the top buns and serve immediately.