Heat half the oil in a non-stick pan over medium-low heat. Brown the pastrami on both sides. Place the cheese on top and melt. Then portion onto the English muffin.
Add the remaining oil to the pan. Crack the eggs into the pan and cook until they start to set. Break the yolks and flip the eggs over to cook through. Season with salt and pepper. Once cooked, place on the English muffin and serve with plum.