As far as I know in the Geeta Lord Krishna never said "Among the Varnas..I am a Brahmana"
Check out the list below:
0. I am the Self, O Gudakesha, seated in the hearts of all beings! I am the beginning, the middle and also the end of all beings.
21. Among the (twelve) Adityas, I am Vishnu; among the luminaries, the radiant sun; I am Marichi among the (seven or forty-nine) Maruts; among stars the moon am I.
22. Among the Vedas I am the Sama Veda; I am Vasava among the gods; among the senses I am the mind; and I am intelligence among living beings.
23. And, among the Rudras I am Shankara; among the Yakshas and Rakshasas, the Lord of wealth (Kubera); among the Vasus I am Pavaka (fire); and among the (seven) mountains I am the Meru.
24. And, among the household priests (of kings), O Arjuna, know Me to be the chief, Brihaspati; among the army generals I am Skanda; among lakes I am the ocean!
25. Among the great sages I am Bhrigu; among words I am the monosyllable Om; among sacrifices I am the sacrifice of silent repetition; among immovable things the Himalayas I am.
26. Among the trees (I am) the peepul; among the divine sages I am Narada; among Gandharvas I am Chitraratha; among the perfected the sage Kapila.
27. Know Me as Ucchaisravas, born of nectar among horses; among lordly elephants (I am) the Airavata; and among men, the king.
28. Among weapons I am the thunderbolt; among cows I am the wish-fulfilling cow called Surabhi; I am the progenitor, the god of love; among serpents I am Vasuki.
29. I am Ananta among the Nagas; I am Varuna among water-Deities; Aryaman among the manes I am; I am Yama among the governors.
30. And, I am Prahlad among the demons; among the reckoners I am time; among beasts I am their king, the lion; and Garuda among birds.
31. Among the purifiers (or the speeders) I am the wind; Rama among the warriors am I; among the fishes I am the shark; among the streams I am the Ganga.
32. Among creations I am the beginning, the middle and also the end, O Arjuna! Among the sciences I am the science of the Self; and I am logic among controversialists.
33. Among the letters of the alphabet, the letter “A” I am, and the dual among the compounds. I am verily the inexhaustible or everlasting time; I am the dispenser (of the fruits of actions), having faces in all directions.
34. And I am all-devouring death, and prosperity of those who are to be prosperous; among feminine qualities (I am) fame, prosperity, speech, memory, intelligence, firmness and forgiveness.
35. Among the hymns also I am the Brihatsaman; among metres Gayatri am I; among the months I am Margasirsa; among seasons (I am) the flowery season.
36. I am the gambling of the fraudulent; I am the splendour of the splendid; I am victory; I am determination (of those who are determined); I am the goodness of the good.
37. Among Vrishnis I am Vasudeva; among the Pandavas I am Arjuna; among sages I am Vyasa; among poets I am Usana, the poet.
38. Among the punishers I am the sceptre; among those who seek victory I am statesmanship; and also among secrets I am silence; knowledge among knowers I am.
39. And whatever is the seed of all beings, that also am I, O Arjuna! There is no being, whether moving or unmoving, that can exist without Me.
Bhavad-Gita