The Prophet ﷺ used to give the salutation to his right and to his left, saying, "Peace be upon you and the mercy of Allah, peace be upon you and the mercy of Allah," until the whiteness of his cheek could be seen.
حدثنا وكيع حدثنا سفيان عن أبي إسحاق عن أبي الأحوص
أن النبي ﷺ كان يسلم عن يمينه وعن يساره السلام عليكم ورحمة الله السلام عليكم ورحمة الله حتى يرى بياض خده
Its isnad is sahih, and it was narrated by the authors of the four Sunans, and Tirmidhi graded it sahih, as in al-Muntaqa 1026, and see 3660.