Sayyiduna Mu'adh bin Jabal (may Allah be pleased with him) narrates: The ablution that the Prophet (peace and blessings be upon him) commanded after eating something cooked on fire means washing both hands and the mouth; it is for cleanliness, and it is not obligatory.
Imam al-Tabarani recorded this report in al-Mu'jam al-Kabir; its chain contains a narrator, Mutarrif bin Mazin, who has been accused of lying.
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب الطهارة / 1329