Whisk eggs and cayenne in a small bowl; season with salt.
Heat the 2 Tbsp butter in a medium saucepan over medium heat. As soon as it begins to foam, add the egg mixture and cook, whisking constantly, until eggs have set in small curds and are beginning to look dry, about 1 minute. Immediately remove from heat and whisk in cream cheese and green onions.
Heat a dry large skillet over medium-low and brush very lightly with butter. Toast English muffins until golden brown and heated through on both sides. (English muffins can be toasted in toaster as an alternate way of heating.)
Place two half slices of bacon on bottom of toasted English muffin, top with ¼ of scrambled egg mixture, one slice of American cheese, and other half of English muffin. Repeat until all four sandwiches are assembled.
