It was the practice of the Prophet (peace and blessings be upon him):
"He (peace and blessings be upon him) would eat with three fingers and lick his hand before wiping it clean."
Hadith Referenceصحیح الجامع الصغیر / حرف الكاف / 4882
Hadith Gradingالألبانی:صحيح
Hadith Takhrij[حم م د] عن كعب بن مالك. الإرواء ١٩٦٩، مختصر مسلم ١٣٠١.