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 2035 a

Abu Huraira reported Allah's Messenger (ﷺ) as saying:

When any one of you eats food he should lick his fingers, for he does not know in what part of the food sticking to his fingers the blessing lies.
وَحَدَّثَنِي مُحَمَّدُ بْنُ حَاتِمٍ، حَدَّثَنَا بَهْزٌ، حَدَّثَنَا وُهَيْبٌ، حَدَّثَنَا سُهَيْلٌ، عَنْ أَبِيهِ، عَنْ أَبِي هُرَيْرَةَ، عَنِ النَّبِيِّ صلى الله عليه وسلم قَالَ ‏ "‏ إِذَا أَكَلَ أَحَدُكُمْ فَلْيَلْعَقْ أَصَابِعَهُ فَإِنَّهُ لاَ يَدْرِي فِي أَيَّتِهِنَّ الْبَرَكَةُ ‏"‏ ‏.‏
Reference : Sahih Muslim 2035a
In-book reference : Book 36, Hadith 181
USC-MSA web (English) reference : Book 23, Hadith 5050
  (deprecated numbering scheme)