This right here is the crux of the whole issue. Your “I” does not think. What we call “I” just knows and is. And while mind ends with death (though the life of each mind is recorded within the very fabric of the universe – see conservation of energy and information), I can never die.
“I” is the very existence itself (the “am”). Obviously, each of us is that “I”, it's why we refer to us as “I” in the first place and why we look at the world from the first person perspective. Thus each of us knows “I am” – we are that.
So your personal identity is “I am”. Period. And your true being and identity is insubstantial, timeless, spaceless, it's that which knows everything (where knowing occurs, there's always “I”), it's the ultimate “ground of being” and yet as personal as it gets, etc. I short, your “I am” is the very “I am” referenced in Exodus 3:14.
There are many ways to verify it for yourself. Psychedelics, sensory deprivation, fasting, various forms of trance, meditation, contemplation, you name it. Since you follow Jesus' way, I will refer you to how-tos in Matthew 6:5-18 and Luke 11:1-13 where these practices are described in detail.
Fasting is pretty straightforward and it can induce altered states of awareness (but it's a pretty harsh way IMO). Prayer as taught by Jesus then consists of contemplative meditation upon the words of Lord's Prayer (there is a specific line that advises not to use it as mantra to induce trance Mt. 6:7-8). Combined together, these two practices create a state of mind conductive to seeing the nature of world and one's “I am”, that is, God.