كتاب الأشربة
36  
The Book of Drinks
(18)
Chapter: It is recommended to lick one's fingers and wipe the bowl, and to eat a piece of food that is dropped after removing any dirt on it. It is disliked to wipe one's hand before licking it, because of the possibility that the blessing of the food may be in that remaining part. The Sunnah is to eat with three fingers
(18)
باب اسْتِحْبَابِ لَعْقِ الأَصَابِعِ وَالْقَصْعَةِ وَأَكْلِ اللُّقْمَةِ السَّاقِطَةِ بَعْدَ مَسْحِ مَا يُصِيبُهَا مِنْ أَذًى وَكَرَاهَةِ مَسْحِ الْيَدِ قَبْلَ لَعْقِهَا
Sahih Muslim 2032 b

Ibn Ka'b b. Malik reported on the authority of his father that the Messenger of Allah (ﷺ) used to eat (food) with three fingers and he licked his hand before wiping it (with towel).

حَدَّثَنَا يَحْيَى بْنُ يَحْيَى، أَخْبَرَنَا أَبُو مُعَاوِيَةَ، عَنْ هِشَامِ بْنِ عُرْوَةَ، عَنْ عَبْدِ الرَّحْمَنِ، بْنِ سَعْدٍ عَنِ ابْنِ كَعْبِ بْنِ مَالِكٍ، عَنْ أَبِيهِ، قَالَ كَانَ رَسُولُ اللَّهِ صلى الله عليه وسلم يَأْكُلُ بِثَلاَثِ أَصَابِعَ وَيَلْعَقُ يَدَهُ قَبْلَ أَنْ يَمْسَحَهَا ‏.‏
Reference : Sahih Muslim 2032b
In-book reference : Book 36, Hadith 171
USC-MSA web (English) reference : Book 23, Hadith 5040
  (deprecated numbering scheme)