Heat a nonstick pan on medium heat. Once hot, add half of the oil and brown the pastrami slices on both sides. Once browned place on the bread.
Add the remaining oil to the pan, along with the eggs and cheese. Move the eggs using circular motions with a spatula or wooden spoon to fluff up and cook, (move the pan on and off the heat as needed to prevent the eggs from overcooking or drying out). Remove the pan from the heat while the eggs are still moist. Season with pepper. (Pastrami is salty so use salt as needed).
Portion the eggs onto the pastrami. Garnish with tarragon. Serve with strawberries.