Whisk the eggnog and nutmeg in a shallow bowl. Unwrap the sandwiches and dip in the eggnog, turning to coat both sides. Melt half of the butter in a large nonstick skillet over medium heat. Add the sandwiches and cook until the undersides are golden, 3 to 4 minutes. Add the remaining butter, flip the sandwiches and cook until golden on the other side, about 3 more minutes.