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 2033 a

Jabir reported that Allah's Messenger (ﷺ) commanded the licking of fingers and the dish, saying:

You do not know in what portion the blessing lies."
وَحَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا سُفْيَانُ بْنُ عُيَيْنَةَ، عَنْ أَبِي الزُّبَيْرِ، عَنْ جَابِرٍ، أَنَّ النَّبِيَّ صلى الله عليه وسلم أَمَرَ بِلَعْقِ الأَصَابِعِ وَالصَّحْفَةِ وَقَالَ ‏ "‏ إِنَّكُمْ لاَ تَدْرُونَ فِي أَيِّهِ الْبَرَكَةُ ‏"‏ ‏.‏
Reference : Sahih Muslim 2033a
In-book reference : Book 36, Hadith 174
USC-MSA web (English) reference : Book 23, Hadith 5043
  (deprecated numbering scheme)