Melt the butter in a large nonstick skillet over medium heat. Add the pastrami and sauté for 2 to 3 minutes. Turn the heat down to low. Combine the eggs with the milk and a few pinches of salt and pepper. Whisk lightly, then add to the pan. Use a wooden spoon to constantly stir the eggs, scraping from the bottom as they set, as they'll continue to cook once removed from the stovetop. Place a slice of Swiss on the bottom of each English muffin. Divide the scrambled eggs among the muffins, top with the muffin tops, and serve.