Essence is a good choice.
But is “un-changing”, the nature of this essence, or is it the “un-interrupted” nature of that essence that is at stake.
Is it about unvariance, or un-continuity? - without variation or without interruption?
Indian philosophy starts with the Ṛg Veda. The book of hymns, the epic, the roaming of the gods. This is the gist of that philosophy. A constantly going activity; of which Ātman is the principal “subject”, across the Veda.
“At”, in atta, comes from √ अत् at in Ātman, which means “to go constantly” (and also to roam). And such is the meaning of the √ at in the Pali; viz. to roam.
Nicca comes from नित्य nitya, meaning “on & on” [PTS] - continual , perpetual , eternal (RV.) [MW].
(or maybe even from निज nija, meaning constant , continual (AV. - Br. - MBh.) ?
The activity of the Buddhist “world” (anthropomorphised in the Ṛg,) is not “going constantly”, says Buddha. Therefore, that activity must be stilled and abandonned, because delusive. Stilled as to escape it.
Is there a “Self” that is “going constantly”? - and what is it? - what is the essential nature of this blissful “constantly going activity” without dukkha?
No need to speculate about that, says Buddha - because that does not help getting out the delusive activity of this “world” (of senses), and the later fine material and immaterial worlds - which are all “un-continuous” - All dhammas arise and fade. They are all discontinuous.
Note: Buddha did hint about a “Self” though - in MN 22:
"There is the case where someone doesn’t have this view:
‘That which is the self is the world (namely the continuous and ubiquitous Ātman/Brāman - of which Ātman is mostly the “subjective” (internal) part - & Brāhman the mostly subjective & objective one). After death this I will be constant, permanent, eternal, not subject to change. I will stay just like that (namely “as I am now”,) for an eternity.’ (In other words, what I see in this world of senses, is that Ātman/Brāhman, with which I must be totally in unison).
He does not think thus: ‘So I shall be annihilated! So I shall perish! So I shall be no more!’ (namely that there is nothing “else” - like a “Self”).
“That is how there is no agitation (MA=fear & craving,) about what is non-existent internally”_ (evaṃ kho, bhikkhu, ajjhattaṃ asati aparitassanā hoti).
Anyway, this possible “Self” behind nibbana - (the unsayable “Self”, on which we would not be able to put a name) - would definitely not be an “unchanging” self.
But a “Self”, whose (constantly going) activity, would have nothing in common with the activities delineated in paṭiccasamuppāda. The latter activities being inherently full of dukkha - therefore with no bliss.