How to Make It
In a medium bowl, combine the ground chuck with the sausage just until they are thoroughly mixed. Form the meat into four 4-inch patties, about 3/4 inch thick. Season the patties with salt and pepper.
In a large cast-iron skillet, heat the olive oil until shimmering. Add the patties to the skillet and press down slightly with a spatula to flatten them to a 1/2-inch thickness. Cook the patties over moderately high heat until very crusty on the bottom, 2 to 3 minutes. Flip the patties and cook until well browned, about 2 minutes more. Top each patty with 2 slices of the Monterey Jack cheese and add the water to the skillet. Cover the skillet and cook over moderate heat until the cheese slices are melted and the burgers are cooked all the way through, 1 to 2 minutes.
Set the cheeseburgers on the toasted buns and top with the cilantro leaves and sliced pickled peppers. Close the burgers and serve right away.