Sharpening your ability to reflect on your sense of self is the path of kings. Self-reflection is the domain of taking perspective. Having this overview effect is like looking onto earth from a spaceship. You are gaining perspective and stillness that is awe-inspiring to most that have the luck to experience it.
Your mind has a special space for reflection. We are entering an area that is dedicated to cognition and sense-making. In other words the Self-knowledge concerning the manner in which emotions, thoughts, beliefs, and other factors are shaping your subjective experience and sense of self. Your Ability to reflect on how subjective experiences of emotions, thought and beliefs shape your sense of self and others.
This capacity for meta-cognition can be trained. And intermediate meditators spend a lot of time on it. On the advanced track of your meditative journey - this will take the shape of deconstructing and unlearning false ideas of how you saw and constructed the self.
The understanding that people don't share the same thoughts and feelings as you do develops during childhood, and is called “Theory of Mind”. Think of “theory of mind” as someone’s ability to “tune-in” to other peoples' perspectives.
Dedicated self-reflection training can be found in all contemplative traditions. If you want to train the traditional way you can try analytical meditation (Buddhism), Dzogchen Training ( Buddhism) or Ramana Mahrshi’s self-enquiry. Modern approaches can be found in the perspective training of Tania Singer’s Resource Perspective Training or Prof. Richards Davidson’s Insight Module. Especially in this advance field of mental training working with a teacher will be extremely helpful.
Training your ability for self-reflection enhances your capacity for meta-cognition, changing perspective and deconstructing perception. You will be able to take a bird eye perspective on challenging situation and empathise with how others perceive the world different from you.