Thank you Metis for this great initiation.
(What follows is my understanding only but many advaitins will have similar understanding/opinion).
This is based on Vedic
sruti '
Tat Tvam Asi" .. or "
Thou art That", which however is not very straight forward. Neither the import of 'Thou' nor the import of 'That' can be mentally realised, and especially since all minds exist with different levels of understanding and hence there are many layers of explanation/understanding of "Tat Tvam Asi".
I believe the same. There are many minds -- following varieties of desires -- but all subsist on the same "I Am" awareness to begin with. The "I am" awareness is said to rise as a singular awareness from the so-called ocean that Hindus call Brahman. The "I am" is all pervasive. Then, depending on particular desires attributes differentiate a single awareness into infinite roles, projected on a mirror called mana (mind). As a metaphor, it is somewhat similar to a single moon being reflected in many puddles.
This is also explained in terms of a single ocean with many waves that come and go but which are essentially all shapes of water. This is a metaphor.
This is most crucial.
Some think that Sankara equates 'You' (individual self)' and 'That' (Ishwara-God). Actually No. 'You' refers to an individual who has no Godlike attribute. OTOH, 'That' is God, Ishwara, full of infinite qualities. As per Sankara, when all attributes are stripped off from both 'You' and 'God',
the attribute-less common general aspect that remains is Brahman, which is said to be of the nature of "ekaadvittiyam, satyam, anantam, jnanam" (ekaadvittiyam is ONE WITHOUT A SECOND; satyam is True, anantam is infinite, and jnanam is of the nature of knowledge/consciousness/awareness).
For example, a wave is not the ocean. But a wave (if endowed with awareness) may realise that its shape is only a temporary phenomenon but that its reality is the reality of the ocean also. Alternately, not realising the oneness of itself with the ocean the wave may face great painful destruction and die out.
So, from the perspective of an individual who is still entrenched with the idea of self being a physical body, the Dvaita Guru, Madhava teaches "You are not that". When this is the knowledge state of an individual, Hinduism generally prescribes "Work without motivation" or "Submission to the Ishwara (God)".
But. But. The scriptures also teach
"Ayam Atman Brahman" (This self is Brahman) and exhort individuals to "Know that Brahman" in order to obtain release from painful cycle of repeated births and deaths.
How does one know 'That', which your own self (and everyone else's) and is 'indivisible one without a second'. One cannot know this as a second entity outside of one's own awareness/consciousness/self, without invalidating and breaking the sruti definition of Brahman.
Atman-Brahman can only be known in non dual awareness without any boundary whatsoever. This is usually called samadhi. Gita says that the truth is known in samadhi only.
YMMV.