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 2031 b

Ibn 'Abbas reported Allah's Messenger (ﷺ) as saying:

When any one of you eats food he should not wipe his hand until he has licked it or have it licked.
حَدَّثَنِي هَارُونُ بْنُ عَبْدِ اللَّهِ، حَدَّثَنَا حَجَّاجُ بْنُ مُحَمَّدٍ، ح وَحَدَّثَنَا عَبْدُ بْنُ حُمَيْدٍ، أَخْبَرَنِي أَبُو عَاصِمٍ، جَمِيعًا عَنِ ابْنِ جُرَيْجٍ، ح وَحَدَّثَنَا زُهَيْرُ بْنُ حَرْبٍ، - وَاللَّفْظُ لَهُ - حَدَّثَنَا رَوْحُ بْنُ عُبَادَةَ، حَدَّثَنَا ابْنُ جُرَيْجٍ، قَالَ سَمِعْتُ عَطَاءً، يَقُولُ سَمِعْتُ ابْنَ عَبَّاسٍ، يَقُولُ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏ "‏ إِذَا أَكَلَ أَحَدُكُمْ مِنَ الطَّعَامِ فَلاَ يَمْسَحْ يَدَهُ حَتَّى يَلْعَقَهَا أَوْ يُلْعِقَهَا ‏"‏ ‏.‏
Reference : Sahih Muslim 2031b
In-book reference : Book 36, Hadith 169
USC-MSA web (English) reference : Book 23, Hadith 5038
  (deprecated numbering scheme)