I was looking for that passage on putting aside self and not-self:
"Where you don't draw a line to define self, there's no line to define not-self. Where there's no clinging, there's no need for the strategy of not-self. So strategies of self or not-self are put aside. At this point, the mind no longer has need for any strategies at all because it has found a happiness that's truly solid. It's not a phenomenon, its a happiness. That Buddha calls it a special form of consciousness that doesn't need to be experienced though the six senses, or what he calls "the all". Its directly experienced as total freedom. And at the moment of awakening, there's no experience of the six senses. However, after the moment of awakening, when the mind returns to the experience of the senses, this sense of freedom stays."
unconditioned consciousness = special form of consciousness that doesn't need to be experienced though the six senses. Now, I'm not going to pretend to understand this, being outside of time, but I'm also not going to jump to calling it a soul or core mind.
If that is too metaphysical perhaps:
Nibbana is asankhata, “unconditioned,” because there is no further conditioning - sankhata - by hatred, greed and ignorance.
There is the Unborn, Uncreated, Unconditioned and Unformed. If there were not, there would be no escape discerned from that which is born, created, conditioned and formed. - Ud 8.3, Iti 43
Ajahn Amaro, The Island:
It is significant that, when the Buddha makes such statements as these, he uses a different Pali verb ‘to be’ than the usual one. The vast majority of uses of
the verb employ the Pali ‘hoti’; this is the ordinary type of being, implying existence in time and space: I am happy; she is a fine horse; the house is small; the days are long. In these passages just quoted, when the Buddha makes his rare
but emphatic metaphysical statements, he uses the verb ‘atthi’ instead. It still means ‘to be’ but some Buddhist scholars (notably Peter Harvey) insist that there
is a different order of being implied: that it points to a reality which transcends the customary bounds of time, space, duality and individuality.