Place a large (about 12-inch) nonstick skillet over medium heat, then add the butter and allow it to melt. Meanwhile, mix the eggs, milk, a pinch of salt and pepper, plus the green chiles and pimientos, if using, in a small pitcher. Pour into the skillet. Add the bread to the eggs, quickly coating the first side of the bread in the eggs (as you would French toast), then turn it over, placing it back in the eggs.
Allow the eggs to almost set completely, about 2 minutes. Using a spatula, flip the whole omelet over in one motion. Top each piece of bread with the cheese, if using. Fold the side edges of the omelet over the bread, then flip one piece of the bread onto the other, creating a sandwich. Allow the bottom of the sandwich to become toasted and golden, about a minute, then flip the sandwich over and cook until the other side is nice and golden, an additional minute.
Remove from the skillet and cut in half. Serve with ketchup or spicy mustard if desired.